"Computational problems" isn't the most informative answer (P2P program is supposed to use only your internets connection, not your processor), so, I am asking here: why in the name of Chuck Norris Bitcoin is using my CPU so much? What is it actually doing?
P2P programs don't have to be bandwidth limited. It just happens that the majority of widely deployed P2P networks do file transfers and are limited by your connection speed.
The computation work to data transferred is more like distributed computing projects like SETI@Home or Folding@Home rather than file transfer.
Suffice it to say that it is verifying transactions and cryptography strength hashes are computationally expensive, and this is good for the value of a bitcoin. For further detail, again, see the paper or the source code.