Summer is the warmest season of the year between the tropics and the poles. (Indeed, it is the warmest season slightly inside of the tropics, too.) This means that June is a Summer month in the Northern hemisphere, and December is a Summer month in the Southern hemisphere.
The warmth is a combination of two factors: the length of the day, and the altitude the sun reaches above the horizon. The longer the day and the higher the sun, the more heat received per unit area on the Earth's surface.
Near the Equator, Summer solstice and Winter solstice actually have less direct sunlight during the day than the equinoxes, so the common model of the four seasons is of limited use at low latitudes. (Every day on the equator is the same length, however on the solstices the sun does not rise as far above the horizon.)
Currently, aphelion is just a few days from the Northern hemisphere's Summer solstice. This means that when the Northern hemisphere is tipped towards the sun, the Earth is slightly further away, and when it is tipped away the Earth is slightly closer. The distance from the sun has only a small effect on the temperature because the eccentricity of the orbit is close to 1, but it does have some effect - so seasons in the northern hemisphere are marginally milder than in the southern. (Aphelion and perihelion are moving very slowly relative to the solstices and equinoxes, in an effect known as precession of the equinoxes, so this will change in a few thousand years.)