The roots of each of your teeth are encased in your jawbone. Each tooth's hole in the bone is termed a "tooth socket." A tooth is held in its socket by way of a ligament which physically binds the tooth in place.
During a tooth extraction a dentist must both enlarge (expand) the tooth socket and also separate the tooth from the ligament that binds it in place.
The term "pulling" a tooth is really a bit of a misnomer. If you have ever tried to remove a tent stake which has been driven deeply into the ground you know you can't just pull the stake straight up to remove it. Instead you will first have to rock the stake back and forth so to widen (expand) the hole in which it is lodged. Once the hole has been enlarged enough the stake can then be easily removed.
A part of the tooth extraction process is somewhat the same. A dentist will use their dental instruments in a fashion that applies pressure to a tooth so to rock it back and forth. This motion enlarges the tooth's socket because the bone that holds a tooth in place is compressible. Once the tooth's socket has been expanded enough the tooth can then be removed.
In addition to a rocking motion, a dentist will also rotate a tooth back and forth. This action helps to rip and tear the tooth from the ligament that binds it in place in its socket. During the extraction process, once the socket has been enlarged enough and the tooth has been separated from its ligament the tooth will come out.