To understand the difference between a single-malt scotch and a double-malt scotch, some whiskey terms must be explained. However, the simple explanation is that a single-malt scotch comes from only one distillery and often refers to scotch that comes from one batch. A double-malt scotch is less common -- it is what is referred to as a vatted malt whiskey. This means that it is a blend of two batches from two distilleries (although many vatted whiskeys will use more than two).
'Scotch' and 'Malt'
Scotch has Scottish origins. Whiskey itself originates in the British Isles, and it was one of the few liquors that a person could legally buy during the Great Depression, for medical purposes. Malted whiskey or scotch refers to a whiskey that has been made from a malted, or fermented, barley.
A single-malt scotch or whiskey comes from one distillery. It tends to be more expensive, and it's associated with quality brands of scotch and whiskey. There are further specialized whiskeys -- a single-cask single-malt is a malt whiskey that has all come from one single cask. This makes a whiskey with a taste limited in nature -- a distillery will sometimes mix different batches and casks to achieve a more consistent flavor.
Vatted malt whiskey is a made from a mix of whiskeys that come from more than one distillery -- two at the minimum, or more. This is done to achieve a consistent product that can always be relied upon to taste approximately the same, which cannot always be said of the more expensive single-malts. It also can be a less expensive whiskey option.
Double is a term that some vendors are using to refer to a vatted malt scotch that has been blended from only two distilleries. Double scotch malt companies will generally tell you which distilleries they used and why they blended the whiskeys together.