Muzzle velocity is, simply, the velocity of a bullet or other projectile at the moment it leaves the barrel of the gun which fired it - the velocity it has when it passes the muzzle. It is expressed in relation to the firing weapon. This value is important in the study of ballistics; it will determine to a great degree both the range and, along with the projectile mass, the maximum energy it can transfer upon impact. This, in turn will affect the terminal ballistics of the shot - how it will affect the target. It is determined by a number of factors, including (but not limited to) the power of the propellant charge; the mass of the projectile and the length of the barrel.
For several examples of representative muzzle velocities, see the Ballistics node.