Generally, a personal exemption reduces the taxable income on a return.
You can claim a personal exemption for yourself unless someone else can claim you as a dependent. Note that’s if they can claim you, not whether they actually do. If you qualify as someone else’s dependent, you can’t claim the personal exemption even if they don’t actually claim you on their return.
Additionally, in order to claim a personal exemption, you will have to file a tax return. If your gross income is over the filing threshold and no one can claim you as a dependent, you can claim a personal exemption for yourself when you file your return.
You can also claim an exemption for your spouse if you file a joint return. However, if you both are nonresident aliens (other than a resident of Canada or Mexico, or certain residents of India or South Korea), you may only claim one personal exemption on the tax return. These restrictions don’t apply if you are a nonresident alien married to a U.S. citizen or if you are a resident alien who has chosen to be treated as a resident of the United States.
If you file a separate return you can claim an exemption for your spouse only if your spouse had no gross income, is not filing his or her own return and was not the dependent of another taxpayer (even if the spouse is not actually claimed by another taxpayer). If your spouse meets these rules, you can claim an exemption for your spouse on a separate return even if he or she is a nonresident alien, as long as they have a tax identification number.
Note that if you have any dependents, you can generally claim a dependent exemption for them if they meet the qualifying child or qualifying relative test. Source