Dear means a few things in different context. If you say it to a person e.g. "Hello Dear" it means you regard them with deep affection. In British English it can also mean something is expensive e.g. "That's very dear" would mean that is very expensive.
Dearest means a similar thing but implies that thing is the most of the dear things. For example, a dear friend would be a close friend. Your "Dearest" friend would be your most dear friend. In the other usage, you could say all the jewelry in a certain shop is very dear, but a particular necklace is the "Dearest" (as in, more dear than the other dear things)