In brief here is what they are:
Bumpmapping is the technique of creating the illusion of ridges, valleys, a non-flat appearance on otherwise flat surfaces.
Per-Pixel Specular Lighting uses texture mapping to calculate lighting with specular (and diffuse?) highlighting, i.e. renders light to a surface.
Post Process Bloom Filtering is a technique to add generate glare or blur over various elements.
High Resolution Compressed Textures. Simply high-resolution textures in a compressed format, which reduces memory and hard drive space usage.
Environment Mapping is a rendering technique used to create more realistic looking reflections on surfaces, which might include cube and-or sphere environment mapping.
Full Shader Model 2.0 support. Support for SM2.0, if your video card supports it.
Custom Pixel and Vertex Shaders for all meshes and effects.
Multiple resolution support is simply saying it provides support for different display/monitor resolutions.
Advanced Particle System something do with advanced FX (effect) particles, which would be weapon fire, visual damage queues, etc.
Self-Illumination is when you see a source of light from a texture map even when the rest of the textured surface is dark due to shadows, lack of light, etc.
Multi-sampling is one of the many anti-aliasing techniques, which appeared around the GeForce 3 genre of VGA cards. This superseded supersampling of the GeForce 2 genre.
Anti-aliasing is the technique of minimizing jagged or blocky (aliasing) patterns, which in essence makes the game world models and textures look smoother.
Edit: Thought some of this was explained well-enough above the quoted material in the actual FAQ.
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