The first is singular and the second is plural so it's the difference between just one lot and many lots. However, "lot" can be a synonym for "collection", making it a collective noun, thereby blurring the distinction between singular and plural. "Lots" just means a collection of collections, which is nothing more than a collection. The end result is that there is no difference in meaning whatsoever.

In many cases they can be used interchangeably. You could say, "I have a lot of apples," or "I have lots of apples". They mean the same thing. For use as an adverb, I prefer "a lot". For example, "I go to the movies a lot." I can imagine someone saying, "I go to the movies lots.", but I don't like that last sentence, and it sounds wrong. Overall, the answer is that they mean the same thing when you see them or hear them used, but there are some differences regarding which you should use yourself. If there are rules, I hope someone else here can help better if there are any rules, but in the meantime, I suggest always using "a lot". I think in any case where you can use "lots", you could have said "a lot", but not the other way around.