Péter is a colloquial word whose primary meaning is “to fart”. The derived noun (“a fart”) is un pet.
It also has another very common meaning: it is a synonym of casser, “to break”.
J’ai pété un verre.
I broke a glass.
Elle s’est pété la jambe au ski.
She broke her leg while skiing.
It can also mean “to explode”.
Un homme a menacé de « tout faire péter » avec une grenade. (Source)
A man threatened to “blow everything up” with a hand grenade.
Péter also occurs in many expressions. One of them is se la péter, which means “to brag”. Don’t ask me what la refers to, just learn it as a set phrase.
Il se la pète depuis qu’il a son diplôme.
He’s been bragging since he got his diploma.
Finally, faire péter can mean “to blow something up” like in the example above, but it is also a very informal way to say “to give” or “to bring”.
Fais péter une bière !
Gimme a beer!
Listen to the examples: