IPFS doesn't actually build on top of the Bittorrent protocol, but rather takes several good ideas from protocols like Bittorrent, Git, SFS, Bitcoin and the web, and gathers them all into one package.
There are several advantages to using IPFS over torrents, but the main advantage is the fact that there is only a single massive swarm, where anybody can give a block to everybody.
For example, say you're visiting a small website that uses jQuery (or some other popular library). There might be only a couple people who visited that website, but you'll still get the library nearly instantly. Maybe from your neighbor, or maybe you already have jQuery in your IPFS repo.
The net result is, the website loads way quicker than would otherwise be possible.