I was never great at this part of the topic either, but I can try to help.
Basically, Westinghouse bought the rights of AC electricity from Tesla because Tesla was reluctant - and didn't have the money - to promote AC. Edison had already been developing DC and was promoting and selling it to people that lived within a few hundred or so metres from his house, where the DC generator he'd built was situated.
AC voltage could be stepped up or down to minimise power loss or be safer around urban and suburban areas, respectively. DC electricity had huge power losses over long distances, hence the reason why Edison could only sell it to people within a close vicinity of the generator. Ultimately, the reason why AC won was because of it's flexibility and relative safety compared to DC.
If anyone else has anything to add, feel free. I may have forgotten to write a fair bit...