As you may know, there are some substances that can be dissolved in water (think about salt or sugar: you can put a spoonful of salt into a glass of water and stir, and eventually the salt disappears! It hasn't actually disappeared, of course; it's just been dissolved into the water). This dissolving happens when the individual atoms or molecules of the solid substance (called the "solute") mix with the individual molecules of water (called the "solvent"). The result is what is called a "solution".

However, there is a limit to how much solute you can dissolve in a given amount of solvent (if you try to add too much salt to the glass of water, eventually it will stop dissolving). When the amount of solute becomes too high, it wants to start leaving the solution and forming a separate solid again. It does this by a process called "precipitation": the individual atoms or molecules of the solute will start to attach to one another and form small crystals; as more and more atoms attach to these crystals, they become bigger and bigger.

To go back to the salt example, imagine that you dissolve as much salt as you can into the glass of water. Now, if you leave the glass out, the water will start to evaporate, but the amount of salt in the water will remain the same. That means that some of the salt needs to leave the solution, since the smaller amount of water can't hold it all. So the salt will start to form crystals of salt; eventually, once all of the water has evaporated, all that will be left in the glass are crystals of salt.