The tournament series are the monthly tournaments that take place in Guild Wars between eight member guild teams as well as one versus one battles. The tournaments not only pay out with recognition as being one of the best players or being a member of one of the best guilds in the game, but also with tangible rewards from the Zaishen faction. Some of the rewards include titles as well as special emotes and potions.
The full list of rules can be found on the main Guild Wars site, under the competitive section. It's a long read, but a necessary one for anyone interested in participating in this year's tournament series.