A launcher is like a custom UI that sits on top of Android. TouchWiz is an example of one, as is HTC Sense on HTC phones, but they're not particularly good examples as many people seem to dislike them. Apex and Nova are both really good IMO, and are designed for ICS devices.
This is probably the craziest one I've seen, although I found it too complicated to use and it's also expensive: -
http://www.youtube.com/watch?v=SYzYQ6YtepU
I use Apex because it basically adds extra options and functionality, but without changing the fundamental way you do things (other than making certain tasks simpler).
Most launchers are either free or they have a free version that has a couple of features locked behind a pay wall. You can easily test a launcher out by downloading it from the market, then instead of pressing "Open" once it's installed, press the home key on your phone. It will ask which launcher you want to use, so choose the one you just installed and then you can play around with it. Any customisations you make while using that launcher do not affect your home screens in the standard launcher/UI, so if you don't like the new one, uninstalling it will take you back to how the phone was before you installed it. If you like a particular launcher, you can make it the default.
The only thing you really lose is the odd widget, for instance, HTC Sense has some widgets that are exclusive to that launcher, so if you switched to Apex, when you look at your widget list the HTC Sense widgets would not be available to add to your home screens, but you can usually find equivalent widgets in the Google Play store.