The military derivation is a little different from everyday use, which is to start out earlier than your rival. That might not gain you a great deal. In military terms it was much more advantageous to squeeze in an extra, surprise march which would advance your troops to a position many miles ahead of where the enemy would expect them to be.
A general would not wish to rush into engaging the enemy when his own troops would probably be fatigued, but they could take up a defensive position ready to ambush the enemy or prepare for a surprise attack at the first opportunity.