"Any" is used when there are three or more choices to choose from, and it doesn't matter which one is chosen. For example, a conversation may go like this:
Person 1: "Would you like toast, eggs, cereal, pancakes or bacon for breakfast?"
Person 2: "Any."
This would mean that person 2 is happy to have one of those choices, with out preferring one over another. In this case, person 1 would choose what to give person 2 for breakfast. If there were only two choices, the conversation would go like this:
Person 1: "Would you like toast or eggs for breakfast?"
Person 2: "Either."
"Either" has exactly the same meaning as "any", but it is only used when there are two choices.
I can't think of a very good explanation for "some", especially so because "some" and "any" can in particular sentences be swapped, while the sentence has the same meaning. I'll wait and see if any one comes and offers one, otherwise I'll try my best at that as well.