Bone is a unique tissue in the body. Even though it seems solid, like wood, it is slowly and constantly being dissolved and reformed. So the bone you have now is actually not the same bone you had a few years ago. Orthodontics is able to move teeth because bone has this quality of constantly being reformed. If gentle pressure is applied to a tooth for a long enough time, the bone surrounding the tooth will change shape. One side of the tooth socket will feel pressure and the bone here slowly dissolves. The other side of the socket feels pulling or stretching, and this causes new bone to form. Slowly but surely, the tooth will move with new bone and gums forming around it.
Orthodontic treatment takes many months or even several years because the speed of tooth movement is limited by the rate of bone dissolving/reforming, which is fairly slow. By the way, a thumb sucker can make their front teeth stick out by this same process. If the thumb pushes against the teeth for long enough time, the bone around the teeth will slowly reform creating an overbite.