Terminology 
Analytic sampling
This is one of the VRay's techniques for calculating motion blur. Instead of taking a number of time samples, the analytic method blurs the moving triangles perfectly. It will take in consideration all triangles crossing a given ray during a given time interval. Keep in mind that because of its "perfection" this method will be extremely slow on highpoly scenes with fast motion. (See also: Motion blur parameters, Motion blur, Quasi Monte Carlo sampling)
Antialiasing (Image sampling)
Antialiasing is a special technique for producing smooth images of highcontrast edges and small details in materials and objects. VRay achieves antialiasing by taking additional image samples where necessary. To determine if more samples are needed, VRay compares differences in color (and/or other properties) of neighboring image samples.. This comparison can be performed in several ways. VRay supports fixed, simple 2 level and adaptive antialiasing (See also: Image samplers parameters, GBuffer, GBuffer Antialiasing)
Area lights
Area light is a term describing a nonpoint light source. These types of light sources produce area shadows. VRay supports rendering of area lights through VRayLight. (See also: VRayLight parameters, Area shadows)
Area shadows (Soft shadows)
Area shadows are blurred shadows (or shadows with blurred edges) that are caused by nonpoint light sources (Area lights). VRay is capable of producing the effect of area shadows either through VRayShadow or through area lights. (See also: VRayShadow parameters, Area lights)
BRDF (BiDirectional Reflectance Distribution Function)
One of the most general means to characterize the reflection properties of a surface is by use of the bidirectional reflection distribution function (BRDF), a function which defines the spectral and spatial reflection characteristic of a surface. VRay supports the following BRDF types: Phong, Blinn, Ward. (See also: VRayMtl)
BSP (BSP Tree, Binary Space Partitioning Tree)
BSP is special data structure for organizing scene geometry in order to speed up raytriangle intersections (intersecting a ray with the triangles in the scene is the task most frequently performed by a raytracer). Currently VRay implements two types of BSP Tree. These are a static BSP Tree for scenes without motion blur and a motion blur BSP Tree. (See also: Motion Blur)
Bucket (Region, Rendering region)
A bucket is a rectangular part of the current frame that is rendered independently from other buckets. The division of a frame into rendering regions allows for optimal resource utilization (CPUs, PCs, memory). It also allows for distributed rendering. (See also: Distributed rendering)
Caustics (Radiosity)
This is the effect of light refracted by a nonopaque object hitting a (diffuse) surface. (See also: Caustics parameters)
Depth of field (DOF)
Depth of field is the effect of having a particular point in the scene to appear focused (sharp) and the rest to out of focus (blurry) depending on camera shutter properties and the distance from the camera. This is similar to how real world cameras work so this effect is especially useful for producing photorealistic images. (See also: Camera parameters)
Distributed rendering is a technique for utilization of all available computational resources (all CPUs in a machine, all machines in a LAN, etc.). DR divides the currently processed frame into rendering regions and keeps all CPUs in LANconnected machines busy computing the rendering result. Overall DR assures that VRay makes the most out of your equipment when rendering a single frame. For animation sequences however, you should use MAX's standard network rendering as it may be more efficient. (See also: Bucket, Distributed rendering)
Early termination is a technique for reducing the samples taken for evaluating a blurry value. This basically works by looking at the samples as they are computed one by one and deciding, after each new sample, if more samples are required. Early termination is used throughout VRay for all blurry values. See also importance sampling.
GBuffer
This term describes the collection of various data generated during image rendering. These could be Zvalues, material IDs, object IDs, nonclamped colors etc. This has proven to be very useful for performing postrendering image processing. (See also: GBuffer parameters, Antialiasing, Image samplers parameters)
GBuffer Antialiasing
VRay is capable of antialiasing the rendered image based on the differences in one or several GBuffer channels. (See also: Antialiasing, Image sampler parameters, GBuffer)
HDRI (High Dynamic Range Image)
A High Dynamic Range Image is an image containing highdynamic range colors (with components exceeding the range 0.01.0, or 0255). This type of images is often used as an environment map to light the scene with natural light.
Importance sampling is a technique for basing the number of samples required for evaluating a blurry value, on the effect that value has on the final result. For example, dark materials require fewer samples for evaluating GI than bright materials; dim area lights can do with less samples than bright lights etc. Importance sampling is used throughout VRay for all blurry values. See also early termination.
Index of Refraction (IOR)
The index of refraction is defined as the speed of light in vacuum divided by the speed of light in a given medium. IOR = C/V, where V is the light speed specific for the different mediums. To achieve a material with a specific IOR you have to set the Index of refraction field value in MAX's standard materials in the section Extended parameters.
Material  Index 
Vacuum 

Air at STP 

Ice 

Water at 20 C 

Acetone 

Ethyl alcohol 

Sugar solution(30%) 

Fluorite 

Fused quartz 

Glycerin 

Sugar solution (80%) 

Typical crown glass 

Crown glasses 

Spectacle crown, C1 

Sodium chloride 

Polystyrene 

Carbon disulfide 

Flint glasses 

Heavy flint glass 

Extra dense flint, EDF3 

Methylene iodide 

Sapphire 

Heaviest flint glass 

Diamond 

Indirect Illumination (Global lighting, Global Illumination)
In real world when a particle ray of light hits an object it produces multiple reflected rays with different intensity in all directions. These rays on their turn may hit some other objects and produce even more rays and so on. This process, multiply repeated, generates the so called Global Illumination. (See also: Indirect Illumination parameters, Irradiance map)
Irradiance map
Indirect Illumination in VRay is generally achieved by calculating GI samples. The irradiance map is a special cache where VRay keeps precalculated GI samples. During the rendering process when VRay needs a particular GI sample it computes it by interpolating the nearest precalculated GI samples stored in the irradiance map. Once computed, the Irradiance map can be saved in a file and reused in subsequent renderings. This can be especially useful for camera flythrough animations. Samples for VRayLight can also be stored in the irradiance map. (See also: Indirect Illumination parameters, Indirect Illumination, Area lights, Area shadows)
Low accuracy computations
In certain cases VRay will not need to compute absolutely precisely a ray contribution to the final image. VRay will then use faster but less precise methods for computation and will take fewer samples. This produces slightly noisier results, but decreases rendering times. Users can control the degree of optimization by changing when VRay switches to Low accuracy computations by changing Degrade depth values. (See also: Degrade depth, Low subdivs)
(Quasi) Monte Carlo sampling
Monte Carlo sampling is a method for numerical computation of integrals of functions by evaluating these functions at a number of random points. Quasi Monte Carlo sampling is a modification of this method, which instead of randomly generated points uses points forming a lowdiscrepancy sequence, which are more evenly distributed than purely random ones. This is the method used by VRay to evaluate complex things like global illumination, blurry reflections, depth of field, motion blur and image antialiasing.
Motion Blur
This effect is observed when looking at some fastmoving object. The motion is so fast that one can not focus the object and the object's image appears blurred to the viewer. (See also: Motion Blur parameters, Analytic sampling, Monte Carlo sampling)
Photon, Photon map
This is a simulation of a real world photons (a photon is a light particle). In order to produce caustics effects VRay traces certain amount of photons that come out of the light sources. Then the results are stored in a photon map and used during the rendering process so that highly realistic caustic effects are produced.
Reflections
As an advanced raytracer VRay supports accurate reflections. Glossy reflections are as well supported (See also: VRayMap parameters, VRayMtl parameters, Glossiness, Reflections, VRayMtl)
Refractions
Refraction is the bending of a wave when it enters a medium where it's speed is different. The refraction of light when it passes from a fast medium to a slow medium bends the light ray toward the normal to the boundary between the two media. As an advanced raytracer VRay supports true accurate refractions. VRay also handles glossy refractions (See also: VRayMap parameters, VRayMtl parameters, IOR, Translucency, Glossiness, Reflections, VRayMtl)
This is a technique for..?
In VRay subdivs is a measure for the maximum amount of samples (rays) that VRay will use to compute a certain value. The maximum number of samples is proportional to the square of the subdivs value. For example, if the subdivs value of a glossy reflection is 5, VRay will never make more than 5 x 5 = 25 samples to evaluate the reflection.
Translucency
Translucency is a term describing the interaction of light with a nonopaque medium (wax, marble, skin etc.). VRay supports a simple translucency model that can nevertheless produce quite natural results. (See also: VRayMap parameters, VRayMtl parameters, Refractions)