Why does FFT output need to conjugate processing? I came across some matlab code as the below,

fftout   = fft(adc_in, 1024); 
fftout_p = fftout.*conj(fftout);


I think fftout is formatted as complex form. from here I'm ok.

Next stage that signal is multiplicated by itself which is conjugated.

I think it means that it want to get the real number not complex number.

From here, I'm not sure and want to know that practically what does Imaginary part affect to real signal processing?

Can we ignore like above that? 

In real practically engineer field, What do conjugating and Imaginary part mean and affect to the real engineer field?
The real part represents cosine correlation, and the imaginary coefficient represent the sine correlation.  Cosines are even or symmetric functions in the DFT aperture, and sines are odd functions (or anti-symmetric) in the DFT aperture.  So you can only ignore the imaginary coefficients for exactly symmetric input.

Conjugation and multiplication is “just” a mathematical trick (identity) to compute sin^2 + cos^2 which is the hypotenuse squared (Pythagoras).