A comb filter is a specific type of filter which operates by adding a delayed version of the signal back to itself. The frequency response has a repeating pattern of notches or spikes, like a comb, hence the name. The signal difference you show above is sort of like that in that it is mostly low-pass filtering -- the "normal" speech sine wave is of low frequency compared to components of the "lisp part" one, but there is still high frequency content in the "normal" signal.
Generally deessing is implemented by using bandpass filtering to isolate frequencies between ~2kHz to ~10kHz and using that signal to control a compressor such that those frequencies are made less prominent but not constantly attenuated. There are many ways to implement a band pass filter. (See: https://en.wikipedia.org/wiki/De-essing .)
A Fourier transform converts between time domain and frequency domain. Time domain is what you are looking at in your signals above. Frequency domain is another very useful way to visualize a signal. This page describes the spectral display function in Audacity: http://manual.audacityteam.org/man/spectrogram_view.html . (You can get more information on the underlying algorithm for making such a display by looking up the "short-time Fourier transform" or STFT.)
Also, generally "smoothing" in signal processing means some form of low-pass filtering. With images, we call this "blurring." In practice, we want the smoothing to have some useful properties for preserving content -- such as being able to understand the speech after removing noise. The preservation requirements usually require something more sophisticated than straight low-pass.
