A monkey is any member of either the New World monkeys or Old World monkeys, two of the three groupings of simian primates, the third group being the apes. There are 264 known extant species of monkey.
Since you were not specifice in your question I will talk about all "monkeys" in general. There are two main groups of monkeys Old Wolrd and New World.
New World monkeys live in South America while Old World are from Africa and Asia. Some characteristics are shared among the groups; most New World monkeys have flexiblen grabbing tails tails while Old World monkeys have tails or no visible tail at all. Some have trichromatic colour vision like that of humans, others are dichromats or monochromats. Although both the New and Old World monkeys, like the apes, have forward facing eyes, the faces of Old World and New World monkeys look very different, though again, each group shares some features such as the types of noses, cheeks and rumps. In order to understand the monkeys, it is necessary to study the characteristics of the different groups individually.
Some live in trees and some live on savannahs and depending where they live there diets differ among the various species but may contain any of the following: fruit, leaves, seeds, nuts, flowers, insects, spiders, eggs and small animals.
Chimps for example mainly eat fruits but also eat meat and have been seen to cannibalize enemy chimp groups. Some types of baboons live completely off savannah grass. Gorillas live off forest greens while most New World monkeys live off forest fruits.