Persephone and demeter have a great love for one another. Demeter always likes to stay close to her lovely daughter.
Persephone is noticed by everyone, even Hades! He wants to make her his queen. So one day he decides to come up to earth and kidnap Persephone and take her down to the underworld.
Hades and Persephone make it safely down to the underworld and poor Demeter has know idea where her daughter is. She grows old in a short period of time and since she is the goddess of the weather, everything grows cold and trees lose their leaves.
Demeter finds out that persephone is in the underworld, and she alerts Zeus. Zeus calls on Hermes the messenger god to go and tell Hades that he must return Persephone. Persephone is found and sent back up, so the weather turns back to nice and hot.
Hades tells Zeus that Persephone ate the fruit of the dead so she must stay in the underworld. Zeus says she will stay there 1 month for every pomogranite seed she ate from the underworld.
So for the first half of the year during summer and spring the weather is beautiful because Demeter is with Persephone. But for the second part of the year Persephone must stay in the underworld with Hades, and whenever not with her, Demeter is sad and causes autumn and winter. This is how the Ancient Greeks believed to have caused the seasons