Think of it as a distributed filesystem with content addressable by hash values. If you want to publish some content instead of posting a torrent file and seeding it, you can announce the content on IPFS to your IPFS peers. Anyone else can now find it by hash (or by name if you use IPNS). If anyone else downloads it, like with a torrent, they'll begin sharing it back out creating redundancy and, potentially, reducing access time for others as more people are sharing it out (imagine you're on a 10Mbps network connection and the only one sharing it versus having 100 others sharing it out, even if they're also all on 10Mbps connections it will be faster). Content can be "pinned" which ensures it remains on your IPFS node, if it's unpinned anything you download will eventually disappear (basically an LRU cache). So if you download the entire run of Dungeon Magazine but don't pin it, it will disappear if you continue downloading content via IPFS when the cache you've set aside for IPFS fills up (eventually). But if you pin it, the content will remain hosted by your node indefinitely, even if no one ever accesses it or pins it again and the original disappears.

Filecoin is a separate thing (mostly), and can (kind of) be thought of as pinning-as-a-service. It's built on a private IPFS network, not the main public one most people use or are directed to. So it's using IPFS, but it is not IPFS.

Is there a client that I can run and point at an existing file structure to make it all available on via IPFS? Perhaps with limiting on outgoing bandwidth?