There could be a couple of different reasons some people leave their garage doors slightly ajar.
Letting in some air to drain off some of the heat in the garage wouldn’t necessarily make the house itself hotter, but it could keep the garage cooler, especially if there were a breeze blowing from the right direction. And it’s possible some people might have some heat-sensitive junk stored in the garage or maybe something that doesn’t smell so great.
But probably the main reason: garage-door openers.
Hot air rises, right? It’s probably hot enough in your garage as it is, assuming it’s not air-conditioned. But up near the ceiling it’s a lot hotter. Many garage-door openers come equipped with a heat sensor that sort of pulls the plug on the opener when the mechanism gets too hot. That’s to prevent fires. So leaving your door up a few inches helps keep the garage a bit ventilated. Of course, you don’t want to leave it up high enough for a burglar to wiggle under it.
If you don’t like the idea of leaving the door up a few inches and you’re having an over-heating problem with your opener, you could install a couple of roof vents to funnel off that hot air.