What Trillian is, is it's a client which has plugins which allow it to communicate with the MSN servers, Yahoo! servers, AIM, ICQ, and IRC servers (and more).
Let's just say you had an MSN account and a Yahoo account and you wanted to talk to one person who had MSN and one person who had Yahoo, and you didn't want to clutter up your PC with tonnes of IM software, then you could just download and install Trillian, so you could communicate with these two people in one program.
That's basically it. Also, if you had two MSN addresses, perhaps one for people you knew as in worked with, or whatever, and one for people who you'd met online but weren't sure about, you could connect to both of these at the same time.