I have a n18 year old who doesn't know what to claim on her w-2.What does it mean to claim exempt on your w-2/

An exemption = dependent (one you support). The number of dependents one has determines how much federal and state tax gets withheld from one's pays check. The more dependents one has the less the government withholds for taxes. For example: If a man has a wife and two children, he can claim four exemptions. If you daughter is single with no children, she can claim one exemption.

Not sure if this is what you meant, but:

If your daughter is asking about how to fill out her W4 form (not W2) for a new job, then to claim to be exempt means that she had no tax liability for 2008 and believes she would have no tax liability in 2009 despite her wages. If she isn't sure about that, I would recommend taking two allowances per the normal instructions:
www.irs.gov/pub/irs-pdf/fw4.pdf