Okay, first of all, let’s debunk this myth right now: alot is not a word. Not in English, anyway. It’s not even an accepted alternate spelling of a lot. It just does not exist.
I think we all know what a lot means, so I’ll move on to allot. Totally different concept, even though it’s pronounced the same. To allot something is to divide it into portions. One might, for example, allot a certain amount to families, while individuals might receive a smaller allotment (the noun form of the word). Allot is a synonym for apportion. Makes a lot of sense, right?