To understand the difference between summer and winter solstices, we need to have a clear understanding of the word solstice. We know that earth revolves around sun in an elliptical orbit, but it also spins around its own axis. This is an imaginary line going right across the planet from North Pole to South Pole. Fortunately for our planet, this axis is not perpendicular but tilted about 23.5 degrees and it is this tilt that gives us seasons on earth. This tilt makes one half of earth receive more direct rays from sun than the other half which remains away from earth.
The axis, when it tilts towards the sun, it makes northern hemisphere receive more direct rays from the sun than southern hemisphere. This phenomenon occurs between June and September and thus this is the period when it is summer season in the northern hemisphere. Again, this axis tilts away from the sun between December and March which is why we have winter season in the northern hemisphere during this period. While it is summers in northern hemisphere as it receives more direct rays from the sun, it is winter in the southern hemisphere, and vice versa in winters.