Your teeth are surrounded by bone under the gums. It is this boney support that holds them in place.

They are attached to the bone with very short ligaments. Lots of little fibers connecting root to tooth. These fibers don't flex very much, but it's enough to give you a sensation of biting pressure, and so that your teeth naturally can move just a little.

It is possible for the ligaments connecting your tooth to bone to die and the tooth and bone connect directly together. Hard to remove a tooth like this.

Gum tissue attaches to your teeth as well, and can hold on pretty tight, but this sort of attachment alone isn't enough to keep your teeth from falling out during use.