'AltiVec' (as Motorola calls it), 'VMX' (as IBM calls it), and 'Velocity Engine' (Apple's term for it) are the same thing: one or more (depending on the processor) 128-bit-wide vector processing units which are featured by the Motorola G4 and IBM PPC 970 processors.
Code written specifically for these vector processing units can speed up certain operations (e.g. manipulation of multimedia data) by a tremendous degree. Those who want a full explanation of how it operates should have a look at this article.
