Answer
Because of differences in the amount of sunlight received in the summer and winter due to the tilt of the Earth's axis, it is warmer in the summer than the winter.
Work Step by Step
The Earth's axis of rotation is tilted at an angle of $23.5^{\circ}$ from the vertical as the Earth orbits the sun. For six months of the year, the north pole is tilted toward the sun, and for the other six months of the year, the north pole is tilted away from the sun.
When the north pole is tilted toward the sun, the northern hemisphere receives sunlight for more than a $180^{\circ}$ rotation of the Earth, that is, for more than twelve hours each day. Also, the sun is higher in the sky which increases the intensity of the sunlight on the surface These effects are stronger around the summer solstice which is the day of the year with the most hours of sunlight and when the sun is high in the sky.
When the north pole is tilted away from the sun, the northern hemisphere receives sunlight for less than a $180^{\circ}$ rotation of the Earth, that is, for less than twelve hours each day. Also, the sun is lower in the sky which decreases the intensity of the sunlight on the surface These effects are stronger around the winter solstice which is the day of the year with the fewest hours of sunlight and when the sun is low in the sky.
Therefore, because of differences in the amount of sunlight received in the summer and winter, it is warmer in the summer than the winter.
Note that a similar explanation can be given for the southern hemisphere.
