Adolf Hitler was, apparently, Eddie's mother. The fact that the Nazi dictator died in 1945 and neither had children or in fact was he a woman, one must assume that the Adolf mentioned by Eddie had only the name in common.
Eddie's mother has been mentioned seldomly throughout the series, often with contradicting explanations of her place in his life. In "Burglary", Eddie explains to Richie that he was abandoned on a doorstep with an old service revolver and a note saying "please look after my baby, I can't be bothered." He twice infers that her forename was Adolf, first in "'s Up" and later in "Digger." Also in S'Up, he tells Richie that she was a wrestler. How he could have known all of this despite being abandoned is not clear, although in "Burglary" he says he regularly read about her antics in the tabloids.
At some point prior to the events of Bottom Live: The Big Number 2 Tour, she died and left Eddie mustard gas, cyanide pills and a giant man-trap baited with a pint of lager and a packet of cheese and onion crisps. Eddie later used the mustard gas along with his Great Uncle Susan's homemade vodka to make Love Gas into order to make Richie win over the Queen.