Why is summer warm - is the Earth closer to the Sun?

It is the tilt, and the distance actually works the other way. The Earth's axis leans about 23.4 degrees, so for half the year your hemisphere is angled towards the Sun. That does two things: the light arrives more steeply, concentrating the same energy on less ground, and the day is longer, so there is more time to heat up and less to cool down.

The distance explanation fails on the simplest test. The Earth is at its furthest from the Sun in early July and its closest in early January - so the northern hemisphere's summer happens when we are furthest away. And if distance were the cause, both hemispheres would have summer at the same time, which is emphatically not what happens in Australia at Christmas.

The tilt itself came from something violent. The leading account is that a Mars-sized body struck the young Earth, knocking it over and throwing up the debris that became the Moon. The Moon has since stabilised that tilt, holding it within a narrow range, where Mars - with no large moon - wobbles across tens of degrees over millions of years and has correspondingly chaotic climate history.