It means you are stating under oath that you had no federal income tax liability last year, and don't expect to have any this year. If you are a dependent and will make under $5450 total income for the year, then that's OK to put "exempt".
They won't take any federal income tax out of your paycheck that way. If you end up actually having tax liability for the year, you'll have to pay when you file your return, and could be fined for illegally claiming "exempt".
The Target people should not tell you to put exempt unless they know you didn't have other income this year to take you over the limit. If this is your first job, and is part-time, you are most likely OK. But next year, if you are going to work ALL year, you might need to change it to zero. The limit for next year will probably be more than $5450, but not a lot.