It depends on which of the L5R game products you mean. There is a Collectible Card Game, or CCG, in which you build a deck of collectible cards, then use it to fight against opponents and their decks. Depending on how you build your deck, you may win by crushing your opponent Militarily, by gaining so much Honor that you simply come to dominate Rokugan's politics, by manipulating and slandering your opponent so that he loses so much Honor that he ceases to be a contender for control of the Empire, or--hardest of all--by getting all five of the so-called Elemental Rings into play and winning by becoming Enlightened. The choice is yours!
There is also an L5R Role Playing Game, or RPG, in which you and your friends assume the personae of Rokugani samurai and undertake perilous quests in the tumultuous world of Rokugan. A Game Master acts as a sort of "referee", posing challenges and adjudicating, using the rules of the RPG, the outcomes of your actions.
Finally, there are various other L5R gaming products. For example, there is a board game called Ninja, in which you play stealthy ninja of the Scorpion Clan trying to outsmart and outmaneuver the vigilant guards of the Lion Clan. There is also an L5R-themed version of the award-winning "micro-game" Love Letter.