Solutions are an important part of everyday life. On a small scale, our bodies are full of solutions such as blood. On a massive scale, the chemistry of salts dissolved in the ocean -- effectively a vast liquid solution -- dictates the nature of oceanic life. Oceans and other large bodies of water are good examples of unsaturated solutions, in which more salt -- the solute -- can dissolve into the solution.
When a solute crystal is added to an unsaturated solution, individual solute ions or compounds -- depending on the solute -- become surrounded by solvent molecules. The solvent molecules have plenty of space to reorganize themselves in such a fashion in order to dissolve the particle. Even if only one more molecule could be dissolved, the solvent molecules can quickly rearrange to accommodate the last particle before the saturation point. Any further additions, however, would have no space to squeeze into, and the particles would simply float or sink to the bottom of the container.
In most cases, it is possible to dissolve more solute by heating up the solution. Even after subsequently cooling the solution, the crystals will stay dissolved. This is called supersaturation – the solute will only crystallize if an additional crystal is added or the solution is disturbed. That type of crystallization is how rock candy is made.