Apples like all other fruits and vegetables are made up of tiny cells. These cells contain a variety of nutrients in them. Now, there is a diversity of microscopic organisms that feed on these cells. These microscopic organisms are mostly fungus or bacteria. In the case of apple, there are mainly two types of fungi that are responsible for the molding/rotting of apples, they are Penicillium expansum and Monilinia fructigena. These fungi release an enzyme pectinase that breaks down pectin, which holds the cells of apples together. Once the cells break open these fungi derive their nutrients from them and grow. If left unchecked they will grow all over the fruit and make it look moldy. It is always advisable to not eat an apple that has mold on it since it can cause one to get sick.

Mold is a fungal growth. Since fungi cannot make food from sunlight, they must feed on other organic materials, much like animals. Apple and other fruits are full of nutrients and are ideal for fungi to grow. Multicellular fungi will form a filament called hypha. Those hyphae form the mold we can see.

I assume you're asking how it is possible for mold to grow on apples (otherwise this question is much more similar to questions like "why are we here" and "what is the meaning of life"). Mold can grow on apples under certain conditions. First, there needs to be a source of mold, which is not hard -- mold spores (single cells of mold or a small cluster of a few cells that can stay alive for a while and be taken from place to place by air currents) are everywhere. Second, the temperature needs to be good for the mold to grow. Room temperature is usually high enough for mold to start growing after a few days. Third, there needs to be a source of food, and apples, like many other fruits, can be a great source of food for mold spores; apples have moisture (water), which all organisms need, and sugars, on which many different molds thrive. Given these conditions, an apple left on the counter for a few days can easily allow mold to grow. Other foods, such as cheeses, can develop mold, too, and sometimes at temperatures much colder than in a typical room.

Materials that humans cannot eat may even provide nutrients for different types of molds. Of course, we have used mold for making food as well -- cheeses are a great example of this -- and penicillin was developed from a mold.

Mold is a successful living thing, and it reproduces by sending spores into the air. These mold spores are pretty much everywhere, and they grow into fungi when they find a nice place to grow, such as a damaged spot on an apple's skin.

I lived in a moldy apartment once, and after I moved, I unfolded some little towels and found that there was grayish mold on them. ;-[

Molds are fungi that can infect and eat various materials made from plants, including apples.