When your peel, bruise or cut fruits or vegetables, the plant tissue releases some enzymes; there is one called Polyphenol oxidase (PPO, phenolase) which in the presence of oxygen from the air, goes into chemical reactions of plant compounds to give brown pigments known as melanins. This reaction is known as enzymatic browning.

An enzyme is a protein that accelerates the rate of chemical reactions.

Enzymatic browning can be a significant problem, because it limits the shelf life of many fruits and vegetables. However, enzymatic browning is not always unwanted. The browning reaction contributes to the desirable color and flavor of raisins, prunes, coffee, tea, and cocoa.

Although enzymatic browning causes changes in flavor and taste (bitter, astringent), and may reduce quality, the melanins formed are not toxic. Brown fruits are safe to eat for some hours after cutting.

Bananas like other fruits are ripened due to a hormone called ethylene. Ethylene breaks down complex sugars into simple sugars and breaks down pectin, a substance which keeps bananas hard. In addition there are hormones that break down green pigments which you see in un-ripe bananas and replace them with yellow pigments. However as the banana continues to ripen these yellow pigments are broken down and not replaced at all producing the brown color in a process much like that of leaves in deciduous trees (trees which lose their leaves annually) during fall and winter. So brown bananas are a result of over-ripening.