CWM is the shortform of ClockWorkMod. ROMManager, CWM recovery, Tether etc are their products. CWM Recovery and ROMManager are tools which enables you to backup your current ROM, install custom ROMs etc.
If you are interested in knowing more about CWM, see this page. For rooting you do not need CWM. In fact for installing CWM you need to be rooted.
For anyone who plays with ROMs, tweaking and testing, CWM Recovery or some thing equivalent to it is mandatory and would save your neck several times.
Also, you could specify which part you are not clear with. It will help to get better answers. :)