Rather than collecting ore or whatever and trucking it back to your base to fund your war machine (they didn't do too much of that in WWII), you send troops to capture strategic points. By holding these, you gain a steady income of manpower, oil or munitions, depending on the point type.
The Axis and Allied armies are superbly balanced, with the Americans relying on speed and numbers and the Germans specializing in heavy armor. Victory often depends on using the terrain to your advantage - units will automatically take cover behind nearby walls and rubble, a sniper nested in a tower can drop entire squads of infantry before they know what hit them, and a machine gun team can be taken down in a heartbeat if outflanked. Of course, none of them stand a chance against armor without anti-tank weapons or mines.