Why do they put in stitches after tooth extractions?

Get a good clot: Sutures or stitches are sometimes placed to insure good clot formation. This is critical to get good healing started so that any bleeding problems are minimized. Some dissolve in a week, others need to be removed.

To close the wound: The stitches will keep the gums closed over the extraction sockets so it will facilitate healing and also keep the blood clot stable.

Better healing: Approximating the gums helps in faster healing.

Usually not needed: Sutures are not needed after most extraction. Sometimes an incision is made to access the bone or roots of teeth, or sometimes tissue tears in the process. On the cases sutures will be needed. If multiple teeth are being removed, the likelyhood of sutures increases.

Sometimes: Stitches are use to hold tissue where the surgeon wants it. Sometimes we need them and sometimes we don't. It is up to the clinical judgment of the operator.