The Summer Solstice is an astronomical term regarding the position of the Sun in relation to the celestial equator. The Summer Solstice is the date with the longest day and hence with the shortest night. This date usually falls near June 21 (in the Northern hemisphere) or December 21 (in the Southern hemisphere).
At the time of this solstice, the earth is in that point of its orbit at which the hemisphere in question is most tilted towards the sun, causing the sun to appear at its farthest above the celestial equator when viewed from earth.
Midsummer is the time around the summer solstice. There are traditional holidays celebrated in Northern Europe and elsewhere at this time. It is also a sabbat of Neopaganism. Please note that this midsummer is not the middle of summer, if summer is defined as the warm time of year, because of delayed heating effect. Indeed, summer may be defined to begin with the summer solstice.