If you backpack around Europe and are traveling on a budget, you will probably want to stay in a hostel, an inexpensive lodging made typically for young travelers willing to sleep in dorms.
The word hostel comes from the Latin hospitale meaning "inn, large house." Think of a hostel as an inn for students or young people. Often you can stay in one of these places for relatively little money because multiple beds are in one room and you share the bathroom with other guests. If you want to meet traveling students, you could try opening a youth hostel in your home town.