Apple contains an enzyme known as polyphenol oxidase (it is a copper containing enzyme).
When the fruit is cut, this enzyme becomes reactive as it comes into contact with air. It reacts with the sugar present in the fruit and results in the formation of brown colour on the cut surface. If cut apple is dipped in an ascorbic acid solution browning of the cut surface can be prevented as the acid inhibits activity of the enzyme.
Apple contains iron in the form of ferrous ions. These ferrous ions easily oxidize into ferric ions. This ion in the ferric state is brown in colour. When the apple is cut open the ferrous ions on the cut surface are exposed to the air. Air oxidizes them and the resulting ferric ions turn the surface brown.