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A double trigger is an elongated trigger that allows two fingers to rest on the trigger and for either one to pull the trigger and fire the gun.
Advantages
The double trigger allows you to fire with either finger which allows for greater rates of fire. With an appropriate gun and some practice you can "walk" the trigger where one finger pulls the trigger, followed by the second finger and then repeated by the first again - with practice you can walk the trigger and significantly increase your firing rate.
Disadvantages
Unless it comes stock you may be an expensive upgrade, sometimes requiring a new trigger guard or even a new grip. Double triggers also don't really seem to offer much of an advantage in firing faster for many low-end blowback paintball guns sine the trigger pull is so long that you can't effectively walk the trigger.
Preference
Whether or not to use a double trigger boils down to preference. I personally prefer them to a standard trigger, but if I have a gun that comes with a single trigger I don't feel it's worth the price to upgrade to one. Find out what you're comfortable with and stick to it.