With P2P software the reasoning is pretty straight forward, particularly if you're talking about a Bittorrent client as the P2P software. Part of the way you connect to other users who have the file or parts of the file you're trying to get is by incoming connections to your computer, directly to the P2P program. If you're ports are blocked then the program can't listen for incoming connections and you won't connect to nearly as many peers (NAT in hardware firewalls often causes the same problem).
This also poses an obvious risk though: an open port means an open door for a hacker to walk through so there's certainly security to be considered, which is what MS is warning you about.
All that being said, it is typical for most serious users of such software to forward ports in order to have more peer connections and thus increase download and upload speeds, which should only require allowing the program through your firewall without configuring ports, the port gets configured on the hardware end, but the end result is much the same, it does present risks of getting hacked, at least as I understand it it does (anyone who knows more please feel free to correct me and I'll learn something today

).