's can be:
1. An abbreviation for "is", as in: "He's playing."
2. An abbreviation for "has", is in: "She's played."
3. A possessive marker.
The 3rd point is the trickiest, but here are the rules:
If the noun does not end in -s, then you simply add 's:
boy -> the boy's books
girl -> the girl's shoes.
If the noun ends in -s and it is plural, then you simpy add an apostrophe:
boys -> the boys' books
girls -> the girls' shoes
If the noun ends in -s and is singular, then you have a choice. Different people have different ways of doing it.
Some say you should use the apostrophe only:
James -> James' books
Others say you should add the s:
James -> James's books
You will find both.