A double bet is the simplest of the multiple bets. It is two selections in different events where both must win. i.e: Arsenal to beat Man Utd at 2/1 and Red Rum to win The Grand National horse race at 3/1.
If you have a £10 double (or whatever currency) all the winnings from the first selection rolls onto the second selection.
If they both win, in this example you win £20 from the first bet + £10 stake returned = £30. This £30 then goes onto Red Rum at 3/1. When that wins you receive 3 x £30 = £90 + your £30 stake back = £120. You have turned your £10 into £120 in this example.
Another way of looking at a double: Think of a double as two separate bets. Imagine you had a £10 bet on Arsenal to win their football match at 2/1. You get £30 when they win.
Then imagine that you put all that £30 on Red Rum at 3/1. You would get £120 back when the horse won.
A double bet is combining those actions into one bet.
What is a treble?
The same as a double but with three selections in different events. They must all win for you to win the treble bet.