We think you should write children’s books.
As you boil a solution of water and sugar, the water evaporates. Heating it allows the water to dissolve more sugar than it could at room temperature. But, as it evaporates, less and less water is holding the same amount of sugar, and when that happens, it is called a supersaturated solution. This means that the water is holding more dissolved sugar in suspension than it could under normal circumstances.
In a saturated solution, the attraction between the molecules of the water and the sugar are in balance with the attraction the sugar molecules have to each other. If something happens to upset the balance, the sugar molecules are likely to become more attractive to each other and they quickly clump up into crystals, or as you so beautifully put it, rocks. Crystals form until the solution again becomes saturated, meaning that the water is holding just the amount of dissolved sugar that it can at that temperature.
Crystallization can be disastrous; often you have to start over (well, hardly a disaster, but inconvenient and wasteful). If you haven’t burned anything, though and keep heating it, the water is able to hold more sugar as it gets hotter, and some or all of the crystallized sugar is able dissolve in the syrup again.
What can upset the balance in a supersaturated sugar syrup? Anything — a little dust, an errant sugar crystal from the side of the pan, or even stirring. Don’t stir a sugar syrup once it is boiling, it crowds the molecules and tempts those sugar molecules to link up.
So what is the correct process? One of the most important steps is to make sure the sugar is completely dissolved before it comes to a boil — this significantly lessens the chance of making rocks. You should also brush the sides of the pan with a wet pastry brush as it comes to a boil, to wash any sugar crystals down off the sides during cooking. Once the solution comes to a boil, let it boil unmolested until it has reached the desired temperature.