Your sinus cavity is essentially a large hollow airspace, lined by a thin membrane around a thin layer of bone contained within your maxilla/upper jaw. Think of a balloon but with a shell on the outside. The sinus cavity normally sits above the roots of your upper teeth, especially the back teeth where the molars are. Depending on a variety of factors, including variations of normal anatomy, there can be a lot of space/bone in between the roots of your teeth and the sinus, or there can be much less space. In some cases, the roots of your teeth and your sinus cavity have less than a millimeter of bone separating the two. In other cases, the sinus can pneumatize, or expand into the areas in between your teeth, or where your teeth are missing, filling the jaw bone with air space. The only times the sinus is a factor in your dental treatment or health, is in cases of tooth infection spreading to the sinuses, or when the sinuses are in the way of placing a dental implant.
When the sinus is in the way of placing a dental implant, there is not sufficient bone to adequately support a dental implant due to the air space of the sinus cavity. This can be fixed by doing a procedure called a sinus lift. During the procedure, the bone is carefully drilled through without damaging the sinus membrane. The sinus membrane is then lifted, and a bone graft placed underneath. Quite often, a dental implant can be placed the same visit as the sinus lift procedure, so the two can heal together.