A hostel is just like a hotel, except you usually don't get a room (unless you're willing to pony up an extra $20.) You're just looking for a cheap place to stay, but you don't want it to be scary. Hostels generally are not scary at all, and are filled with mostly pleasant foreigners. They used to have rules that require that you have ID proving that you don't live in the town that you're hostelling in, though; don't know if that's changed at all.
The wikipedia entry for hostels kinda sums it up, including the picture of the taiwanese hostel: http://en.wikipedia.org/wiki/Hostel