I was trying to follow and implement a method propose on the research paper. And currently, I have having some trouble to understand the wavelet transform. In particular, the paper I am looking at is "High-Impedance Fault Detection Utilizing A Morlet Wavelet Transform Approach"
And the part I am confuse is depicted on the figures following. 
I am just wondering, how exactly did he get the second figure using Morlet Wavelet transform....What kinds of things is he plotting? The coefficient or what?
When I use CWTFT in MATLAB, it is suppose to return:
Which ones corresponds to the graph he produce?
You should read about the wavelet transform in general. Unlike fourier transform which loses all time dependence and goes completely into the frequency space, and short-time fouerier transform that can observe some variation of frequency with time (but obeying the uncertainty principle), the wavelet transforms select a basis wave (some wave-packed with some oscillatory shape and some envelope) and splits the signal into wavelet components over time and over multiple scales (you can stretch or compress the wavelet to change its frequency). What you get are coefficients that tell you the amplitude of the wavelet at certain time (your time axis) and certain scales. This is what CWT represents. Each column of this matrix is the time dependence of an amplitude at a certain selected scale (which is a roughly similar concept to frequency).
Morlet wavelet is just a particular selection of a basis wavelet: http://en.wikipedia.org/wiki/Morlet_wavelet
Your signal apparently has a mostly consistent frequency. This means that at the scale that makes the basis wavelet have the same periodicity than your signal, you will detect how the amplitude increases at the middle of the signal.