Correct spelling, explanation: the base form of watches is watch and it can function either as a third singular form of the verb or as a plural noun form. Watches is a word with a long history word as it could already be found in Old English, in the forms waecce and waeccende, which could be translated as watchfulness and remaining awake. Later, watches acquired the meaning that it has in modern English.

Definition of watches:
1. noun – a plural form that describes a small clock that you wear on your wrist,
I’ve had many watches in my life, but this one is my favorite one so it’s such a shame it’s broken.
2. verb – third singular form of the Present Simple, refers to looking at something for a period of time,
Every time she’s by the sea, she watches the blue water in silence, which is like a meditation to her.
3. verb – third singular form of the Present Simple, refers to looking at something or someone to make sure it’s safe,
I love shopping at the airports so Jack always watches my luggage.

Phrasal verbs and expressions with watches:
A few popular phrasal verbs and expressions with watches are:
1. watches over someone – to protect someone,
After the last attempt of abduction, a bodyguard watches over the princess all the time.
2. watches out for something – to be careful in order not to miss something interesting,
He watches out for every new book by this author.
3. watches one’s weight – to be careful not to get fatter,
She is so slim, but she still watches her weight, I hope it’s not some kind of an obsession.

Incorrect spelling, explanation: it is true that in most cases when we want to create a plural noun form or the third singular form of the verb in Present Simple, we simply add an -s letter to the word. However, in the case of watches, as a result of the pronunciation, we need to add an -es ending. Some users of English don’t remember about that and they create the form watchs instead of watches, which is wrong.