Yep, as their name suggests they are servers designed for seeding torrents. There are generally two types of seedboxes; dedicated servers and VPS 'slices'. The VPS slices are generally a lot cheaper but you share system resources and bandwidth with other users and dedicated servers are an entire server with dedicated uplink to yourself.
Most servers will offer 100Mbit - 1Gbit uplink capabilities and you generally have traffic limits of between 4TB and 30TB p/m depending on the provider.
Probably the best reason to own one is the security it provides for torrenting. What I mean by this is depending on the country where your server is located the laws regarding file sharing and copyright infringement are less stringent than in your own country... you can see where this is going. Also, grabbing the files via sftp will provide you with an incredible level of security which isn't possible with most other forms of file sharing.
There are a ton of other things you can do with a server, IRC shell, website hosting/selling, private game server hosting, ventrilo, personal VPN/proxy, the list can go on for a while.