It's in P2P networks (e.g. BitTorrent), where people share content. While you download, you offer what you already have downloaded and that's associated with your IP. And that's their attack vector: you're distributing copyrighted content without a license.

After that file hosters (e.g. Rapidshare) became popular, where only one person is uploading and the downloaders are hard to identify and even harder to sue.