There are two ways you can claim a dependent, if you are claiming a qualifying child, they have to be under 19 or under 24 and still a full time student.  A qualifying child does not have an income limit, they just cannot have paid for more than half of their own support.

A qualifying relative has to make less than $4050 in gross income to be considered a dependent. 

The full requirements for qualifying child and qualifying relative can be found in IRS Pub 501.

https://www.irs.gov/publications/p501/ar02.html#en_US_2016_publink1000220868