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Firstly, coal does not become diamond anywhere in nature. What follows is simply the answer to the question.

The carbon atoms have to be re-arranged into a new pattern. Coal (graphite) and diamond are of course both primarily carbon.

Graphite (coal) has the atoms arranged where they are connected on horizontal planes, but not on vertical planes (think of a stack of papers....the atoms are tightly linked in each sheet of paper, but the stack itself can easily be knocked over..this is why graphite is a lubricant, because these sheet easily slide around on each other).

Anyway, to change their atomic ordering into diamond requires high heat and high pressure. The heat breaks down the current bonds to free up the carbon atoms, and energize them to bond covalently (very tight atomic bond formed by sharing an electron) and the pressure helps the carbon atoms form in an ordered and tightly packed fashion...the result is the atoms are re-ordered into a pattern that looks like pyramids stacked together (each pyramid connected at four points with its neighboring pyramid), and it is now diamond.

My example is simplified, but hopefully it conveys the basic changes that must occur.

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