You'll find that it varies from host to host, and this is often indicated on their profile.
Some are excited to meet new people, but can't actually host - so they'll often just say they want to meet you in town for a coffee or similar.
Others will have a bed and a spare room, and can be amazingly generous.
However they do understand that you're travelling, are on a budget, and while they may want to show you around the city, they'll also (usually) be keen to help you enjoy your time while on your budget. Some just want a new person to talk to in the evenings, while others will take you around.
I'd suggest signing up, creating a profile, and then looking around at some of the profiles in the cities you wish to visit. It'll give you an idea of what they're looking for in a guest - often they'll say in their profiles that perhaps they just wish to practise a new language, or they like meeting new people.
As for bringing a gift or taking them to dinner - do whatever feels comfortable, and don't force them into it either. Some cultures it's very important to treat a person when they come to your city/house, while others it's customary to bring something - that will depend on where you go, and is probably a topic for another question. ;)