It's basically a full Linux server, except it's really a virtual machine running on something else. That's just an implementation detail, though.
Anyway, I use Slicehost and the service is great. Very easy to manage via their web interface, and the price is not bad. $10/month for daily and weekly full backups is also a plus. If I fuck up the server miserably, I just press a few buttons and I am back to last night's unfucked version.
Don't worry. You don't need to know what a "Linux slice" is because it's a term barely used by anyone except Slicehost customers. You'll more commonly see such systems referred to as "virtual private servers" or VPSes.
Heck, this very page is #3 on Google for "linux slice" which shows how little the term is used ;-)
I'm checking out Heroku, which seems appropriate for my level. Gracias though.