Do you want the short version or the long version? I do a simplified description in my hub page on How do Solar Panels Work. The short version is that all batteries have one thing in common-- they have an area where there are too many electrons and an area where there too few electrons. When these two areas are connected the electrons flow from the negative where there are too many electrons to the positive where there are too few electrons. What makes batteries different from each other is how they create this situation of too many and too few electrons. Most of them do it by chemical reactions.
If for some reason you wanted a real technical explanation I could do this but I would have to know the exact kind of battery in order to explain the fine details.