That it is the simple things that can make a profound difference--in baking, in bartending, in life--is somewhat of a cliché. It's also true, of course, particularly (and literally) in the case of simple syrup. Simple syrup is, quite simply, a mixture of equal parts of sugar and water that is dissolved over heat and then cooled and stored for future use. It may seem unnecessary--why not just stir in some sugar--at first, but if you consider how difficult it is to dissolve sugar in cold drinks, it makes sense. Making simple syrup is also a way to infuse flavors, as you can make it with vanilla beans, citrus peel, herbs and spices, even chiles.
Bartenders use simple syrup all the time, as it enables them to control the amount of sweetening in cocktails. It's also very handy in making lemonade and aguas frescas. Another lesser known use is in cake-making, as bakers brush simple syrup on layer cakes to keep the crumb moist as well as to infuse flavor. Simple syrup is also used to candy citrus peel and to poach fruit.
You can find good quality purchased simple syrups, but they're ridiculously easy to make. To do so, just combine equal parts of water and sugar in a pan and heat until the sugar is dissolved. You can add flavorings to the mixture before you heat it, or after, depending on what you add. Cool the syrup, then store in the refrigerator, where it can last pretty much indefinitely. For cocktails or aguas frescas, try adding lemon or lime peel to the syrup, or peppercorns or chile peppers. Simple syrup that is brushed on layer cakes is particularly good with cinnamon sticks or vanilla beans added to it; or you might try adding a few tablespoons of liqueur or extracts, or infusing mint or lavender in the warm syrup.