Apostrophes are punctuation marks that serve several purposes, but one of their primary functions is to indicate possession or contraction in written language.
A contraction is a shortened form of a word or group of words that omits certain letters or sounds. In a contraction, an apostrophe represents missing letters. The most common contractions are made up of verbs, auxiliaries, or modals attached to other words:
“He would” = “He’d.”
“I have” = “I’ve.”
“They are” = “They’re.”
“You cannot” = “You can’t.”
Contractions are usually considered to be relatively casual. If you’re writing something very formal, you may want to avoid using them except in cases like o’clock, where the full phrase (of the clock) truly is rare.
The rules about forming possessive nouns probably cause the most apostrophe confusion. They vary a bit, depending on what type of noun you are making into a possessive. Here are the rules of thumb:
For most singular nouns, add -’s:
The dog’s leash
The writer’s desk
The planet’s atmosphere
For most plural nouns, add only an apostrophe:
The dogs’ leashes
The writers’ desks
The planets’ atmospheres
For plural nouns that do not end in s, add -’s:
The children’s toys
The geese’s migration route