The meaning of "might" is hard to explain without using "might"! But it's meaning is similar to "maybe" plus "will". If you say that you "might" do something, it means that it's possible that you will do it.
In this example:
...the second speaker says "I might take you up on that" because he's not sure if his friend is serious about wanting to bet, or maybe he's not sure if he really wants to make the bet himself.