Lets consider this scenario. I have a Samsung Galaxy smartphone which comes with Touchwiz as a default launcher. If I use a different launcher does it run on top of the touchwiz interface or does it disable touchwiz temporarily and run instead of it? What are the advantages/disadvantages of using 3rd party launchers?
A launcher, in simple terms, is an interface for your home screen; it determines the appearance of it, if you like.
If you were to install a 3rd party launcher (Nova is quite common), it would not run on TouchWiz, nor would it uninstall it.
If you do install a new launcher and want to go back to using TouchWiz, it's just a simple matter of tweaking a few settings in the Settings app.
The launcher usually is considered to be the homescreens and app drawer, and they come in all sorts of flavors and designs. When you hear people talk about "stock" Android, this usually is what they're referring to -- homescreens and app drawer unchanged from what Google includes in the open-sourced code.