Simple syrup is one of those things that becomes more and more essential to understand as one ventures deeper into the baking world. It can be used to sweeten drinks, such as lemonade or iced tea. But more importantly, it can be used for things like adding moisture to a dry cake. In my time as a baker, I saw a lot of dry cakes. It wasn't that I or anyone else in the bakery was bad at cakes, the recipes we used were just dry in the first place. I think that this had its advantages. It seemed to me that the cakes had a little more structure, even after they were doused with simple syrup to make them moist as well.
Strictly speaking, simple syrup is as easy to make as its name suggests. Combine equal weights of sugar and water, and heat to dissolve. Wasn't that easy? You don't even need to boil the water, you just need to get the sugar to dissolve into it. You can then cool it and move to a squeeze bottle for later use. What kinds of uses? Well, I think one of the simplest would be to combine the juice of a few lemons or limes with some water, and then add simple syrup to taste. I think I usually do somewhere around six limes with a quart or two of water and about a cup or so of simple syrup. Tastes are subjective, and I'm sure your mileage will vary.
Of course, equal weights is not the rule. It may be what they teach in cooking school, but it's really only a guideline. Many people go by volume, rather than weight. When I make limeade, I frequently use a cup of water and a cup of sugar. The more sugar you use, the more viscous the syrup will be. The less sugar you use, the thinner the syrup will be. Of course, there's a big key here: the liquid that you use doesn't have to be water.
I remember one of my first days in a professional bakery, I had to build several tiramisus for a party that night. One of the ingredients I was instructed to use was part dark rum and part coffee symple syrup. Coffee simple syrup? Easy. I ended up using equal weights hot coffee and sugar. Since the coffee was already hot, all I had to do was stir. Then I mixed with some dark rum and started dousing the cake. We cheated and used cake instead of lady fingers, but you get the idea.
In the time since then, I've made a variety of simple syrups, using anything from plain old water to things like coffee or orange juice. You'd be surprised by the things that you can use simple syrup for. For instance, you might find yourself keeping raspberry simple syrup (equal parts strained raspberry puree and sugar) around just in case you want to make iced tea. The possibilities are nearly endless. The important thing right now is to understand what simple syrup is, and how one can make it. It won't be long before you start discovering various ways to use it.