To have Quickness is to be twice as fast as your peers, in more ways than one.
Quickened units:
Quickness is not to be confused with Swiftness, which only affects Combat Speed. However, the CS bonuses of Quickness and Swiftness do stack; to be specific, the added bonus from Swiftness is applied before the multiplier from Quickness.
Quickness is a Water Buff:
Temporary Quickness is generally preferred over permanent Quickness, due to the doubled rate of Aging. Permanent Quickness is also not that easy to obtain, and is usually controllable (e.g. by not sending people to the Arena). Quickness does not boost the rate of spellcasting - boosting that requires specially-made Items.