As frogboy states in the most recent dev diary:
3. The flags. Scattered across the arena are several different kinds of flags. Controlling flags is absolutely crucial to victory. Control of flags earns your team war points which provide access to better types of reinforcements, upgrades and more. The types of flags are:
a. Flag of Experience. Controlling this flag will result in your team gaining experience at a substantially greater rate.
b. Flag of Celerity. Controlling this flag will result in spells having much shorter cool-down times for your team.
c. Flag of Brilliance. Controlling this flag greatly increases the mana pool for everyone on your team.
d. Flag of Fortitude. Controlling this flag greatly increases the hit points for all Demigods on your team.
e. Flag of Valor. Controlling this flag greatly increases the strength of your reinforcements (hit points, attack, defense, etc.).
Hope that helps. I have no idea what the debilitating flag does, but I think it weakens creeps (just a random guess).