Ballista is one of the forms of Conflict (pvp) in Final Fantasy XI. With the recent wave of patriotism sweeping Vana'diel, the decision was made to reintroduce Conflict as a form of friendly rivalry between the three nations. Ballista is based upon San d'Orian military training exercises that involve participants digging up small stones called Petras to toss into goals called Rooks scattered around the battlefield.
Ballista is FFXI's version of an MMO's PvP. It's not very popular, and doesn't hold much of a candle to other MMORPGs PvP systems, but it can be fun with some friends. Getting the license itself is a simple task. You need only be rank 3 in your nation then talk to some NPCs in each nation.
For details on how to obtain your Ballista License, click here.