I do see that they have interpolated several sinc function peaks What I don't get is how the sinc function comes into the equation? why is sinc used?
To elaborate on Samuel's comment. When you sample a signal the spectrum of that signal will become periodic in the Nyquist frequency. To reconstruct the actual signal, you need to remove all of the frequencies that appear as artifacts of the sampling process. Ideally, this would require a brick-wall low pass filter. In the time domain, this corresponds to the procedure your lecturer mentioned with sinc functions, as sinc is the inverse fourier transform of the rect function.