It is a complex story that cant really be explained in a few sentences.
It mainly follows the whole life of Jon Valjean.
It is set in France around the revolution time.
Many poor people ("the miserables") turn to crime to feed themselves and their families.
John Valjean steals a loaf of bread and is sentenced to years in prison.
He is let out "on license" (has to show a piece of paper wherever he works).
But he ignores this and runs away, eventually working his way up to become a businessman and mayor of a town.
One of his young female workers dies and he adopts her daughter.
Because he has broken his parole the police try to track him down, mainly policeman Javert.
Years later his adopted daughter has grown up, and the youngsters of the town want a revoluotion against the rich and noble.
His adopted daughter falls in love with one of the your revoluionaries.
The rest of the story is about the policeman Javert hunting for Valjean, the your revolutionaries fighting the rich, and a love story beween his adopted daugher and the young revolutionairy.
There is an overview here (which might give away the ending)
http://www.lesmis.com/about/the-story-act-1/