Clover is a supporting plant for grass, as it fixes nitrogen in your soil and competes with other weed. Notice how grass that surrounds patches of clover in your lawn is much greener and faster growing? It also stays green long after grass has gone dormant during hot and dry spells.
You can influence the ratio of clover to grass in your lawn. Clover naturally favours a nitrogen-deficient soil and grass is a nitrogen pig. Therefore, the more clover you have, the better your grass will grow. Clover will self-seed where conditions favour it, but generally grass will out-compete it long-term. Without annual re-seeding clover will slowly die back to a sporadic cover as it creates conditions that favour grass. If you want a lawn that favours grass, mow high and and the grass will gradually take the lead. If you want to lawn that favours clover, cut shorter and re-seed white clover every spring. Clover germinates earlier, and this sets back the grass creating conditions that favour clover.
I've used clover to restore lawns I've inherited that have been mistreated by chemicals and poor
irrigation practices (light/daily irrigation). The clover quickly filled in the bare spots, outcompeting more noxious weeds. Combined with a mulching lawnmower, it will create plenty of organic matter to improve soil structure and nitrogen to create an environment capable of supporting grass. Encourage clover and you'll have a healthier lawn than one without it.