How does salt water help to prevent wisdom tooth extraction hole infections?

The rationale for rinsing with salt water solution is to try to keep the socket clean during a time when it is not comfortable to brush the area. The use of salt in the water is intended to keep the solution "isotonic"-- i.e., the salt in the water makes the water more chemically similar to the natural tissue fluid, so its less irritating than plain water.

Patients are typically told NOT to rinse for the first 12 hours after an extraction so as not to provoke bleeding or disturb the clot while it is forming and hardening over the socket. After that, though, the use of warm saline rinses is soothing and keeps the area cleaner and more hygienic, which is a comfort when there is a blood clot fermenting in the mouth and potentially causing odor.