Correct spelling, explanation: sees derives from Germanic languages and it already appeared in Old English, in which it looked as seon. In contemporary English sees is the Present Simple form of the third person singular of the verb to see. It’s a commonly used verb in both formal and informal contexts.

Definition of sees:
verb (3rd person singular of the Present Simple) – to observe what’s around you; to understand; to watch a film, theatre play, etc.; to visit a place or meet someone,
What he sees is darkness and no way of getting out of the room.
I’m not sure he sees the point of our meeting so maybe we should talk with him about it.
She sees a new episode of her favorite series almost every day.
Jack sees that pub every Friday once he finishes his work.

Collocations and phrases with sees:
Some popular phrases with sees include:
1. sees red – to become very angry,
She sees red every time he comes back home so late.
2. sees stars – to be almost unconscious because you’ve been hit in your head,
That’s an extremely brutal sport so he sees stars at almost every match.
3. sees fit – to think that something is important or good,
Every time her older son visits her, she sees fit to prepare a three-course meal for him.

Incorrect spelling, explanation: when adding an -s ending to a verb many users of English make a mistake by adding an apostrophe before -s. The result is an incorrect form, e.g. see’s. In English we use ‘s only when we want to express possession or when it is a short form of is or has. In other cases, we simply add an -s ending to a word as it happens in sees.