What causes discolored teeth after braces?

Many things: Poor home care during braces, decay from not cleaning well enough when the braces were on. Hopefully it is just surface stain that can be removed with a good cleaning and this assumes they were not discolored before the braces.

Oral hygiene: The brackets from braces cover part of your tooth and also become a food trap. If you do not keep the teeth really clean when you have braces on, the color of the teeth under or around the brackets will be different from where the bracket did not cover your tooth. White spots are the start of decay.

Decalcification : The white spots on the tooth are called decalcification which is normally due to poor cleaning.

Hygiene problems: It's so much harder to clean your teeth with braces in place. If you allow bacteria to collect next to braces, the "bugs" will convert sugars int acids that will damage your tooth enamel. Certain foods can temporarily stain teeth (your dentist can clean this off), as do some pigment producing bacteria. Don't want discoloration? Follow your orthodontist's recommendations to the letter.