Range shows how far a unit can fire. Having a higher range than the enemy gives advantage of attacking the enemy while remaining untouchable.
Artillery units and structures have highest range. But they also have minimal range, where they can't fire. If a unit charges and gets close to them, artillery can't fire at them and is useless. That's why artillery is often backed-up by heavier units to avoid such situations.
To visually see units' range in the battlefield, just select them and press Space. You can change this hotkey from hotkey settings. Unit abilities often have different range than these units.