Surround Sound Processors will do 3 interesting things for you. First they will decode the packed up multi-channel audio formats found on standard DVDs and many HDTV broadcasts. Traditional Dolby Digital and DTS surround audio formats have all the audio for the various speakers packed up into a single stream of digital data -- called a "bitstream". They have to be decoded to recover the audio intended to go to each of your various surround speakers.
Second the Surround Sound Processors will do math on the incoming audio to extract surround sound to drive more speakers than are actually represented in the incoming audio. For example, stereo from most TV programs or from CDs can be processed to drive surround speakers. And even 5.1 surround audio can be processed to drive additional rear speakers in a 7.1 speaker setup. There are different forms of processing out there to do this, but the one most commonly discussed is Dolby Pro Logic IIx.
So you might have a Dolby Digital 5.1 bitstream come in from a DVD or HDTV program which is decoded by the Surround Sound Processor into 5 main speaker audio channels plus a bass effects (LFE) channel, and which is THEN post processed by Dolby Pro Logic IIx math to invent an additional two channels of rear speaker surround sound.
Finally, Surround Sound Processors do what is called speaker configuration management -- including bass steering. This has to do with properly steering audio according to the type and nature of speakers you actually have. So for example, if you don't actually have a front center channel speaker, the processor would steer center channel audio to the front left and front right speakers so you don't lose anything. And if you have a good subwoofer, the processor could also steer bass to the subwoofer that would otherwise have to be played by your main speakers that might not handle bass so well. Additionally, this part of the Surround Sound Processor corrects for the different volume levels produced by each speaker (so that they are properly balanced with each other) and the subtle timing differences due to the speakers not all being at the same distance from your listening position.