Problem

You configure audience targeting for a webpart using AD groups. A newly added user is unable to see the webpart even though you have confirmed that the account has the correct AD group memberships.

Cause

SharePoint updates AD user group memberships only after the User Profile Synchronisation service is run.

Solution

Open Central Administration -> Manage Service Applications -> User Profile Service Application

Start an Incremental synchronisation.

The user should now be able to see the audience targeted webpart.