You can claim an exemption for yourself, your spouse, and each of your dependents. You can generally deduct $4,050 from your adjusted gross income for each exemption you claim in 2017, which will lower your taxable income. 
 
In 2017, the personal exemption will phase out for taxpayers with the following adjusted gross income:

• Married filing joint and qualifying widow(er) $313,800-$436,300
• Head of household $287,650-$410,150
• Single $261,500-$384,000
• Married filing separate $156,900-$218,150

A person who can be claimed as a dependent on another taxpayer's return cannot claim his or her own exemption. 

Per IRS Publication 17 Your Federal Income Tax (For Individuals), page 27:

Overview of the Rules for Claiming an Exemption for a Dependent

• You can't claim any dependents if you (or your spouse, if filing jointly) could be claimed as a dependent by another taxpayer.
• You can't claim a married person who files a joint return as a dependent unless that joint return is filed only to claim a refund of withheld income tax or estimated tax paid.
• You can't claim a person as a dependent unless that person is a U.S. citizen, U.S. resident alien, U.S. national, or a resident of Canada or Mexico. (There is an exception for certain adopted children.)
• You can't claim a person as a dependent unless that person is your qualifying child or qualifying relative.

Tests To Be a Qualifying Child

1. The child must be your son, daughter, stepchild, foster child, brother, sister, half brother, half sister, stepbrother, stepsister, or a descendant of any of them.
2. The child must be (a) under age 19 at the end of the year and younger than you (or your spouse, if filing jointly), (b) under age 24 at the end of the year, a student, and younger than you (or your spouse, if filing jointly) or (c) any age if permanently and totally disabled.
3. The child must have lived with you for more than half of the tax year. (There are exceptions for temporary absences, children who were born or died during the year, children of divorced or separated parents or parents who live apart, and kidnapped children.)
4. The child must not have provided more than half of his or her own support for the year.
5. The child must not be filing a joint return for the year (unless that return is filed only to get a refund of income tax withheld or estimated tax paid.)

If the child meets the rules to be a qualifying child of more than one person, only one person can actually treat the child as a qualifying child.

Tests to Be a Qualifying Relative

1. The person can't be your qualifying child or the qualifying child of any other taxpayer.
2. The person either (a) must be related to you in one of the ways listed under Relatives who do not have to live with you, or (b) must live with you all year as a member of your household (There are exceptions for temporary absences, children who were born or died during the year, children of divorced or separated parents or parents who live apart, and kidnapped children.) (and your relationship must not violate local law).
3. The person's gross income for the year must be less than $4,050. (There is an exception if the person is disabled and has income from a sheltered workshop.)
4. You must provide more than half of the person's total support for the year. (There are exceptions for multiple support agreements, children of divorced or separated parents or parents who live apart, and kidnapped children.)

Page 33: Relatives who don't have to live with you. A person related to you in any of the following ways doesn't have to live with you all year as a member of your household to meet this test.  

• Your child, stepchild, foster child, or a descendant of any of them (for example, your grandchild). (A legally adopted child is considered your child.)
• Your brother, sister, half brother, half sister, stepbrother, or stepsister. 
• Your father, mother, grandparent, or other direct ancestor, but not foster parent. 
• Your stepfather or stepmother. 
• A son or daughter of your brother or sister. 
• A son or daughter of your half brother or half sister.
• A brother or sister of your father or mother.
• Your son-in-law, daughter-in-law, father-in-law, mother-in-law, brother-in-law, or sister-in-law.

Any of these relationships that were established by marriage aren't ended by death or divorce.

Foster child. A foster child is an individual who is placed with you by an authorized placement agency or by judgment, decree, or other order of any court of competent jurisdiction.

You may also wish to utilize the IRS Interactive Tax Assistant (ITA) topic Who can I claim as a dependent?