The World Leaders Tournament comprises of Gym Leaders from all of the regions. Seven of them will be chosen at random, and they'll join you in a single elimination tournament. You'll have to defeat three of them in order to become the victor of the tournament, and since you have no idea what to expect, it should be a good challenge.
If you succeed and defeat three of the World Leaders to win the tournament, you'll receive 1 BP for each Pokemon in your party that isn't knocked out after each round, although you'll gain the BP only if you win the tournament's three matches. This means a Single Battle will net you 3 to 9 BP, a Double Battle will net you 3 to 12, and Triple and Rotation Battles potentially netting more!
Since there are too many Gym Leaders to post on one page here, just refer to the previous tournaments to see which Pokemon they'll be using.
After you've beaten the World Leaders Tournament a total of 10 times, you'll unlock the final challenge: the Champions Tournament!