You will find that you gradually grow hungry. Typing STATUS will show you how hungry you are. If you are well fed, you will gain a health bonus. As your hunger grows, this health bonus will gradually fade away until you begin to starve, as shown on the table below:

utterly satiated       - Gain a 1/9 health bonus.
reasonably full        - Gain a 1/7 health bonus.
not hungry             - Gain a 1/5 health bonus.
feeling a bit peckish  - Gain a 1/3 health bonus.
weak from hunger       - No bonus.
starving to death      - You start to take damage due to starvation.

HELP BUFFS describes the exact details of how health bonuses are applied, but in general the more well fed you are, the higher the maximum bonus to health you will receive.

In order to eat, you will need to find yourself some food - most commonly from a shop run by a cook. Generally speaking, the more expensive the food, the more sustenance value it has, though there is not an exact one-to-one correspondence. Once you have food you may EAT <item> to consume it. On the other hand, you might like to savour it properly, in which case you can SMELL <item> and TASTE <item> to appreciate the hard work your chef put in prior to eating.