The diagram is correct (except that white ellipses illustrating rotation need to be tilted as pointed out by someone), and reason for seasons is earth's tilt.
Consider earth drawn at the left in the diagram. The north pole is towards the sun. You can draw a line from Sun to the north pole. Now imagine the earth is spinning about its AXIS. The point marked as north pole in the diagram stays stationary. Rays from the sun will ALWAYS hit the north pole - meaning sun will never set.
Consider what happens at the South Pole. You cannot draw a ray fom sun to the south pole without it hitting an obstacle. Further - similar to what we saw before, while the earth is spinning about its AXIS, the point marked as south pole stays stationary and is always in the dark - the sun never rises.
Now consider in between points on earth's surface. The points on northern hemisphere are tilted towards the sun. Take any point P on northern hemisphere while its daylight. Draw the normal at this point. Now draw a ray from sun to this point. Measure the angle - theta1.
Now take the point opposite of P on the southern hemisphere. Call it Q. Rotate the earth about its axis by 180 degrees so that Q is now in the line of fire - i.e. facing the sun. Repeat the process. Draw the normal at Q. Now draw a ray from sun to this point. Measure the angle - theta2.
Observe that theta1 < theta2 => This is the reason its summer in north hemisphere and winter in southern hemisphere. Please do the thought process described (calculating theta1 and theta2). Once you do it, it will immediately become clear the reason of seasons.
The situation reverses after 6 months when the southern hemisphere is tilted towards the sun.