Billeting means inviting the Performer to stay overnight at your place. It’s just like letting a friend stay at your place during their travels! Performers are sometimes on the road for many months and motels, hotels, and hostels can wear you down, so the change of pace of sleeping in a guest room/coach/spare floor is often much appreciated. When billeting Performers, some Hosts even go above and beyond by offering meals (after checking about allergies/dietary restrictions), laundry, or tours of local attractions, but what you’re comfortable offering is totally up to you. The bare minimum of a billet would just be allowing a Performer to stay with you for free. What’s important is that they have a private space and they are given time to rest - remember these performances are their work and late night partying might not be in order.
If you’re not comfortable doing that, that’s not a problem! There’s nothing wrong with saying “Sorry, we’re not available to billet this time,” and offering a billet shouldn’t be expected. Folks aren’t entitled to staying with you if that’s not what you’d like to do.
If you have a friend or neighbour who would be interested and available to billet (perhaps in exchange for a guest list spot), and you have made those arrangements in advance, you may communicate that to the Performer, but if not, feel free to suggest an affordable nearby hotel/motel.