Almond syrup is a type of simple syrup flavored primarily with almonds. Almond syrup can be as simple as adding almond extract to simple syrup as it cools, which lends a cherry tinged almond aroma and flavor to the syrup. It can be as complex as making orgeat, which is a multi-day process with results in a golden, translucent syrup with notes of cream and orange flower water that turns off-white when added to cocktails.
Interestingly enough, many stone fruits such as cherries, peaches and apricots have cyanide compounds in them which give them the classical "bitter almond" smell of cyanide.
Torani and 1883 are two brands of commercial almond syrup, which generally are corn syrup sweetened and artificially flavored. Some higher quality brands use apricot kernels to mimic a bitter almond flavor and are sugar-based. B.G. Reynold's Orgeat uses both sugar and apricot kernels in their syrup.