You can do this very easily. If you hover over the name of the tag with your mouse (either in the Recruits or Contacts tab), you will have 2 icons that pop up - one is a pencil and the other is a trash can. If you want to delete the tag, you can click the trash can. If you want to edit the name of the tag, click the pencil and you can change the name to whatever you'd like.

When you delete a tag, you are not deleting any of the contacts in that tag. You are simply removing that tag from any of the contacts listed in it.