Billeting is when the Host invites the Artist to stay overnight at their place after the show. It’s the same as letting a friend stay over. Some Hosts have already indicated in their Space profile that they can billet, but it’s best not to assume that’s the case with every show, so it’s recommended you check in about billeting while confirming the rest of the show details.
First decide for yourself: a) if you need a billet, and b) whether making the show happen is contingent on if they can billet you. If you are traveling for this show and think you can likely arrange accommodations elsewhere for the night if the Host cannot billet, then please proceed with show negotiations. If the Host is unable to billet at that particular time, they may be able to help you make arrangements elsewhere, either with a neighbour or by suggesting an affordable nearby hotel/motel/hostel. When approaching the Host, you could say something along the lines of “I see your profile mentions that you may be able to billet - is it possible to host myself and my guitar player for the night? If not, no pressure, but we will be looking for somewhere to sleep for the night.”
There is no harm in asking. Hosts will understand that you are on the road and they want to be able to help, but be prepared for the fact that the Host may not be able to have you for the night — they might have family in town or are doing renovations on that part of the house, you never know! Planning a show/tour well in advance will allow you to do some research and sort out the details of accommodations.