in IMAP, subscribing to a folder allows you to view that folder along with your inbox, outbox, etc. In other words it marks that foloder hidden or not from your client. Marking a folder for offline use makes your client download any messages stored in a subscribed folder onto your disk for use offline. This takes longer, but you don't have to have a net connection to read through your email.
There's also the ever important "check this folder for new messages" (wording may vary between clients) that will poll that folder in addition to your inbox for new messages automatically.