Today is the Summer Solstice. This is not, as some think, the day when the Earth is closest to the sun, that's almost six months away. This is the day when the Northern Hemisphere has the sun highest in the sky.
This is due to the tilt of the Earth's axis with respect to the orbital plane of the Earth's orbit around the sun. Though this tilt doesn't change, and (to a first approximation) the direction of the tilt doesn't change compared to the background stars. The direction of the tilt compared to the sun does change. This is due to the Earth's motion around the sun.
Today, the axis is tilted toward the sun (as viewed from the north) and so we have the longest day. The sun passes overhead at its 'highest'. From now on, the sun will rise and set further to the south, and it won't get as high in the sky. The days will begin to draw in.
The weather will still get a bit hotter though, as a rule, this is because a lot of the heat in the atmosphere is trapped (if it weren't we'd all freeze at night). This means it takes time to warm the earth up and cool it down again, so the hottest time tends to be after summer solstice, and the coolest after winter solstice.
I used the word 'tends' as local geography can change things, and weather is chaotic anyway!
Above, I used the phrase 'to a first approximation'. This is because the Earth's axis doesn't always point the same way, it wobbles like a top. This is an effect called precession, and is quite complicated, but very familiar. It's the same effect that causes a child's spinning top to wobble.
In the case of the Earth the period of the wobble is some 44000 years (from memory) - this is why on human timescales we don't have to worry about it too much!