A seedbox is basically a dedicated computer for torrents that runs 24x7 seeding many (I've had over 200) torrents for extend periods of time.
At home I have a laptop running a VPN and a torrent program that allows me to access if from a web browser to manage and add torrents. I do this so I don't get copyright notices or slow down my 'daily driver' computer and leave it on all night.
They were very popular when people had slow connections because the seedbox did all the work and where usually on a different internet connection.
Keep in mind the seedbox uses BitTorrent to download the file and seed (must keep our ratios up). You still need to transfer the downloaded files to the computer you want to use them via ftp (sftp if you care about security).
There are many people renting seedboxes online for a fee, or you can get a hosting package and setup your own.
Hope that helps.
To the original question:
I use uTorrent on Ubuntu with 'Private Internet Access' VPN.