It's important to notice that single does not refer to the word malt here, as it would in an ordinary English sentence. Single refers to the distillery only! There are single malt whiskies made from different types of malted barley, confusingly enough! For example, Glenmorangie Signet is made from two types of malt. However, since it is all made from one single distillery, it's still a single malt whisky.
Another important detail to notice is that the distillery may blend together casks in any way they like to make their single malt whisky. In fact, most single malts are made by blending large amounts of casks in order to create a certain flavor profile. As long as all whisky comes from the same distillery and is made from malted barley only, it's a single malt whisky.
There are some related terms that have special (and sometimes confusing) meanings as well:Blended whisky