Untagging removes the link to your name from the post and also takes the post off your profile. The post will still be visible in other places unless the person who posted it takes it down.
If you don’t like something you’re tagged in, you can ask the person to take it down or escalate the issue:
You can also remove a tag from your profile using the Remove From Profileoption.
Removing a tag from your profile means it won’t show on your profile anymore. If you’d like, you can turn on Profile Review to review and approve each tag before it goes on your profile.
If you've upgraded to timeline, the new profile, get help here.