Albergues are hostels for pilgrims. They offer beds (in shared rooms and some have private rooms), bathrooms, a kitchen, and a place to hand wash and dry your clothes.
Public albergues are owned by a local municipal, an organization, or a religious institution. You must show your pilgrim passport to stay, and the facilities are functional but very basic.
Private albergues are owned by an individual or group. Some accept travelers who are not pilgrims. They're nicer and more comfortable than public albergues.
Public: €5 - €8 for shared room Private: €12 - €17 for shared room; €20+ for private room (if available) Some albergues are even donation-based.
Some albergues, usually public ones, do not take reservations. Book 1 - 2 days in advance when possible, especially during peak season (June - August).