Let us continue to consider in the abstract how to solve optimization problems. Suppose you're placed on hilly terrain in a vehicle with tons of controls (e.g. 26 of them) for movement but only sensors for your current position (so you can tell if you're going up or down). Further suppose you wish to ascend to the highest peak. The difficulties you face are the large number of choices and a lack of knowledge of how the choices (controls) interact. What do you do?
Hill-climbing assumes there is a single, smooth hill. In this case, your best choice is to take the steepest step.
But what if there are lots of bumps -- lots of big hills, each with medium hills, each with small hills, etc.? Then hill-climbing is likely to get stuck on a local max, a small hill on a medium hill that is not the biggest hill. The problem with hill-climbing is that being optimistic gets you trapped locally. This is because the ``best'' local choice is always taken, even if to get to the best solution requires taking some steps down. Therefore, one must occasionally take steps ``backwards'', which is what simulated annealing does.