Privileges are abilities to do and see more on the site that you earn with increased reputation.

Privileges control what you can do on Cross Validated SE. Gain more privileges by increasing your reputation (points you receive from your fellow users for posting helpful questions and answers).

Use the privileges tag for questions about privilege notifications and privilege wikis. Milestones for each privilege are available from the help center.

Reference: imported excerpt and wiki from the main Meta Stack Exchange site.