Any plant matter can be composted. Any part of any fruit, vegetable, flower, whatever. If it came from a plant, it can be composted.
That being said, some things take longer to rot than others. I would advise not composting large, hard seeds from things like avocado, mango, apricot, peach, etc., along with hard nut shells like coconut, brazil nuts, walnuts, etc. as these take a long time (several years) to decompose.
Peanut shells and acorns are fine, though. They are soft and rot comparatively quickly.
You shouldn't ever put meat or dairy on the compost, as harmful bacteria can proliferate as they decompose (egg shells are fine, though).
You also shouldn't put cooked food on the compost, even cooked vegetables, as it is likely to attract vermin. Same goes for processed foods like bread.
Other things that are fine to compost include, but are not limited to:
-bedding and droppings from herbivorous pets (hamsters, rabbits, birds, etc.)
-paper and cardboard (torn or scrunched up; don't compost anything with heavy, glossy ink, such as magazines)
-used tea bags and coffee grounds
-old natural fibre clothes (make sure they are 100% natural fibre, that is cotton, wool or silk, and tear into smallish pieces)
-hair (human or pet, it doesn't matter)
-And, of course, any plant matter removed from your garden, etc. (as long as it isn't diseased).