A book could be written about this topic. It is bassically playing each others strength and weaknesses off of each other. Take tanks for example, it is vulnerable alone however an Infantry guy like myself can greatly improve its survivability in a mout envirement. If I get in trouble out on a patrol I can call in an airstrike on an enemy. A ground pounder is needed to plot coordinates for an artillery strike. We are all connected in one way or another and each of us can greatly impact the outcome of a battle. Combined arms creates a synergy, as a whole it is greater then the sum of its parts.
Combined arms is a way of getting past the "paper, rock, scissors" of warfare.