You can configure forum so that it is moderated. It means that all posts must be approved by one of the forum moderators before they are published in the forum.

 

If the check box Forum is moderated is checked, you can add users that should be moderators of this forum.

 

If you're a moderator, you can approve the forum posts in the Forum properties -> Posts section or you can find the list of all posts waiting for your approval on the Forum groups dialog.