Blagger is East End (London) slang for an armed robber. More specifically a professional armed robber, not an opportunist or amateur. Used pseudo-respectfully for the old-school armed robbers, who "loved their mums".
Blaggers carry off blags, typically post-offices, banks and security vans.
The most (in)famous blaggers are Tommy Wisbey, Douglas Goody, James Hussey, Charlie Wilson, Robert Welch, Ronnie Biggs, Roy James, Ronald "Buster" Edwards and Jimmy White. Their blag, The Great Train Robbery, was the biggest robbery of all time. Carried out on the 15th of August 1963, they netted £2.5 million in used notes.
The events leading up to the robbery, and the subsequent capture and suicide of Edwards were dramatised in the film Buster starring Phil Collins.