From Nafziger's 'Imperial Bayonets' and translated from the words of Marshal Ney 'March or Attack by Echelons This manoeuvre is extremely advantageous in war; but it requires a great perfection in the marching of the troops, in order that the attack upon the enemy may be supported with rapidity and intelligence, and that the battalions which refuse to attack may be in a fit state to execute attentively every movement which circumstances may require.' (Nafziger, 1995:147) Essentially the uncommitted battalions are able to support the attack of those committed far easier, it was notoriously difficult to manoeuvre or disengage with troops once they were engaged in combat, so attacking in echelon essentially gave the Brigade the ability to respond to events faster.
Not completely related but being in echelon is extremely useful for forming squares. If two squares are in line they will be shooting into each other when cavalry pass between them, being in echelon avoids this problem. 'Squares were generally positioned in echelon so that they were mutually supporting.' (Nafziger, 1995:51).