Chances are even if you have an Android phone the term launcher is somewhat unfamiliar to you. The launcher, in the most basic terms, is basically what you see on your main screen, it contains all your apps and can start them, hence their full name, application launchers. On most Androids, TouchWiz is what is on it, but there are ways to download others and change what you see to look sweet. I've experimented with a couple and I'll give my input on their quality and whether or not I think you should use them.
I'll start out with probably the most well-known free launcher called GO launcher. I used this one for a couple of days then deleted it. GO launcher is decent, it changes app design, and incorporates a lot of features that make things easier to do, such as auto-folders for apps. It was very simplistic though, and that was my one quarrel with it. It seemed that there was no freedom to a certain extent, and was like backtracking to my Apple days. For that reason I was not a fan of this launcher.
My favorite launcher I've tried thus far is the Next Launcher. Ironically its made by the same developers who created the GO launcher. I just downloaded the free version because the full version costs somewhere around $17, and there's no way I'm paying for that. The 3D effects, even in the free version, were great and so was the graphic design along with it. It has a space background (I used the launcher with that theme) and the app directory was like a capsule. For a free launcher, this was packed with cool features, of which I'm sure would only be surpassed by the paid version.
The third launcher I've tried is called Smart Launcher. Its interesting because you only have one main screen, that has shortcuts to the most used part of your phone, web, texts, camera, etc. Then you can of course look at all your other apps. These are all stored in one place easily accessible from the home screen. Its cool and actually surprisingly efficient, but it was just too odd for me and I think I would rather have a more complex home screen. It did lead me to everything I used the most, including a clock on the main screen. The only time I found it hard to use was when I needed to use another one of my most used apps, like Twitter or Instagram.
If you were looking at different launchers I hope this helped you. As I find and experiment with more launchers I will be sure to write more posts on them. They can really help jazz up your phone up a little and can be pretty cool to show off to your friends.