“To check out” is a phrasal verb which often means: 1. to look at closely or investigate. It is extrememly common in all types of conversations. 2. It can also mean to leave a business or institution by going through an official process. In both cases, the phrasal verb is separable.
Examples definition 1:
We need to check out what the competition is doing a bit more carefully.
Let’s check out that new restaurant this weekend.
Check it out! Isn’t that that actor from TV!
That guy at the bar is totally checking you out – I think he is interested.
Examples definition 2:
When checking out of the hotel, we saw some colleagues from the conference.
I couln’t check the book out of the library because I owed a fine.
In the *check-out line at the supermarket, I remembered that I had forgotten to buy eggs.
* Here it is used as a compound adjective not a phrasal verb.