1) An apostrophe is used to show contractions.
A contraction shows where letters have been omitted. Contractions are commonly used to combine subjects and verbs and to shorten verbs.
We'd wanted to go to the beach for a long time now. (Combines we had)
I'm not happy when it's raining. (Combines I am and it is)
2) An apostrophe is used to show possession.
Possession refers to ownership or when something belongs to something else. Ask yourself who owns what?
Her mother's cousins wanted to throw a big party. (The cousins belong to the mother)
Karen's textbooks got wet in the rain. (The books belong to Karen)
Note - Personal possessive pronouns like his, hers, theirs, ours, yours, or its already show ownership and never take apostrophes. It's always means it is.
3) Apostrophes do not normally indicate plural.
They are only used to indicate plural in special circumstances such as numbers or letters that don't normally have plurals.
The phrase mind your p's and q's means be on your best behavior.
Note - Apostrophes can be used with plurals to indicate several own something. When using an apostrophe with a word that ends in s, use just the apostrophe. Note how s is used in the examples below:
One student owns
Two students own