Basically, a man was shot by the police because he had a loaded gun in his possession and was killed: they first claimed he was shooting at them, but now with post mortem it appears he wasn't. The gangsters he was with were upset by this so burned down a shop and a car.
Then everyone in London started rioting too, and now everyone in the rest of the country is doing it. Most of what you see on TV is not motivated by the shooting, they just want new trainers and a free TV. They know they can get away with it because our police has come under criticism in the past few years for being heavy-handed with protesters so are scared to act strongly. This and also the police chief recently resigned over News Of The World phone hacking allegations: so no one in charge knows how to handle the situation properly.