There are different kinds of Tax exemptions, however, they all can either reduce or eliminate your obligation to pay income tax.
You can claim one personal tax exemption (Married filing jointly gets one exemption each). The exemption reduces your taxable income just like a deduction does, but has fewer restrictions.
You are allowed to take additional exemptions for each dependent you claim.
Non-profit organizations get a tax-exempt status. Although they are not required to pay federal income tax, they must maintain accurate records to keep its status. Donations you make to these organizations usually entitle you to claim a charitable contribution deduction if you itemize