Starvation is a death caused by going an excessive period of time without food. It is a common way for newbies, low-level wizards and those attempting the foodless conduct to die, although it is more common to be killed by a monster while fainted from lack of food.
To reduce the risk of starvation, eat everything you kill which is safe to eat (if your pet will eat it, you normally can too). It is advisable not to linger on cleared levels, where your only food source is the monsters which are randomly generated. Rings and amulets increase your food consumption by 5% each, so if you are low on food you may wish to avoid wearing them. Be especially cautious of rings of regeneration, conflict and hunger, all of which add 50% to your food consumption, and do not carry so much equipment that you are Stressed or worse. Casting spells consumes nutrition unless you are a wizard with Intelligence at least 17.
If you are weak or fainting from hunger and have no food, pray and your god may fill your stomach (deities regard this as a major problem). Polymorphing into a new version of yourself or dying while wearing an amulet of life saving also resets your hunger status.
The stone to flesh spell can turn a boulder into a huge chunk of meat which will take you from Fainting to Satiated (this is mostly useful for Healers).