Some more terms, this time mostly T&L stuff:
Transform: The process of mapping 3d objects from one coordinate system to another. Examples of transforms that can be performed on 3d objects are : rotation, scaling (size change), and translation (moving it around other than rotation). Normally, each transform is represented by a 4x4 matrix - multiple transforms can be concatenated into one by multiplying together the matrices in the appropriate order. The resulting matrix is then used to transform the 3d object to its appropriate size and placement. Mathematically, the transform is performed by taking each vertex in the 3d object, treat its XYZ(W) coodinate as a vector, and multiply that vector by the transform matrix.
Matrix palette skinning [edited according to Simon F's suggestions below]: Transform method where we, for a given body, first compute a set of different matrices, each corresponding to the transform/placement in 3d space of one rigid body part (like e.g. a bone). This set of matrices is referred to as a 'matrix palette'. Then, for each vertex, we specify a set of indices into this matrix palette and a weight for each index. The matrices that are pointed to by the indices are then blended together using the weights for each index. The resulting matrix is then used to transform the vertex's coordinate. The result of using matrix palette skinning on a 3d model is that the parts of the model flow together naturally rather than making the model look like it is composed of a bunch of rigid parts that just happen to be stuck together - the result is a more realistic look on moving organic figures, such as animals and people.
T&L: Transform & Lighting - a set of calculations that are performed on a per-vertex basis, basically applying transforms and lighting calculations to each vertex. Also, computation of texture coordinates for each vertex is counted as part of T&L. 'Hardware T&L' refers to the capability of 3d graphics hardware to perform these calculations - if such functionality is not present in the hardware, the alternative is 'software T&L'. 'Fixed-function' or 'static' T&L refer to T&L implementations that are restricted in what types of calculations they can perform during T&L - typically, the transform is limited to plain 4x4 matrix transform and matrix palette skinning, and the lighting model used for the lighting cannot be changed (typically a variant of Phong lighting).
Vertex shader: Program that is run once for each vertex that is processed. Also used for 3d graphics hardware capable of running such programs. Vertex shading functionality replaces standard 'static' T&L in the 3d pipeline. Vertex shaders can be used to perform a range of effects on the geometry and the lighting of the model, such as non-linear transforms/procedural geometry (e.g. putting waves on water, putting all of the scene into a fisheye view), lighting models other than Phong (simpler models if higher performance is desired, or BRDF models for added realism etc), and setup for certain texturing techniques (like bump-reflection mapping). Uder the DirectX API, version 8 and up, vertex shaders are given version numbers to indicate their exact capabilitites.
