Supercooled water wants to form ice (ice will have a lower potential energy), but it is incapable of doing so. One (rough) analogy you can make is to that of chemical reactions. For example, it is energetically favorable for hydrogen peroxide to decompose into water and oxygen gas. But, this happens at a fairly low rate. However, if you add a catalyst (e.g. manganese dioxide or catalase) the process occurs quite rapidly. Similarly, supercooled water won't crystallize unless nucleators (catalysts) are present to help water in its liquid to solid transition.
Supercooling does have something to do with the ways the atoms and molecules are set up. In liquid water, there are fairly strong bonds between water molecules that give water its surface tension. This surface tension leads to the need for nucleation.
But, yes, the organization of molecules in supercooled water is no different than the organization of molecules in water above 0oC (aside from the average speed of the molecules).