matlab - what is smoothing in very basic terms

What is smoothing and how can I do it?

I have an array in Matlab which is the magnitude spectrum of a speech signal (the magnitude of 128 points of FFT). How do I smooth this using a moving average? From what I understand, I should take a window size of a certain number of elements, take average, and this becomes the new 1st element. Then shift the window to the right by one element, take average which becomes the 2nd element, and so on. Is that really how it works? I am not sure myself since if I do that, in my final result I will have less than 128 elements. So how does it work and how does it help to smooth the data points? Or is there any other way I can do smoothing of data?

EDIT: link to followup question