If elementalists use the elements to damage foes and necromancers use infections and undeath, mesmers take a different approach, using the power of illusion and suggestion to attack their enemies. They attack with many magical spells, but also rely on short-lived illusory copies of themselves to aid them in combat. While a ranger has a permanent pet, and necromancers have minions that can last through multiple battles, most of the phantasms and clones that the mesmer calls into being are eminently disposable, rarely lasting longer than a single battle. In fact, the mesmer has a number of abilities that actually destroy his or her own illusions to damage enemies or gain some sort of short-term buff.
Life’s a party for a mesmer, even when there’s no one else around.
Many mesmer skills will summon an illusion as a side effect of casting; you can possess up to three illusions at a time, but they're fairly fragile. When you have illusions fighting for you, you can shatter them with any of your special function-key skills to gain an effect. Mind Wrack does straightforward damage; Cry of Frustration will give enemies the confusion condition; Diversion will daze your targets; and Distortation will enable you to evade attacks for a short while. The more illusions you shatter, the longer these effects last.
If you increase your Shatter Recharge Rate via traits, that...well, that means that your Shattering skills recharge faster! Obviously!