To check something out has various meanings:-
It can mean to settle your bill before leaving a hotel etc.
For example: I had to check out of the room at 6am!
It can also mean to withdraw (an item) after recording the withdrawal.
For example: One duty of a librarian is to check out books.
Then it may mean to record and total up the prices of and receive payment for (items being purchased) at a retail store.
For example: The cashier checked out and bagged my shopping.
It can also mean to investigate, examine, or look at.
For example: The police checked out his story.
But to check someone out can mean to look at someone of the opposite sex with interest, which is the implication here.
!Note - to check out is also slang for dying.
For example: I'm not ready to check out any time soon.
