Difference between spectrum of signal and amplitude of signal. Fourier Transform

Hello!

I would very much pleased by knowing the following. If you have some signal and than acting to it by fft() Fourier transform, calculate new x-axe and so on. Than we have somehow to normalize the result of our fft() procedure. In this case, as far as I know, we have two options:

1) get amplitude, by

signal_transformed = fft(original_signal)/length(original_signal);
signal_transformed =abs(signal_transformed );

and than plot and we see determined frequency and their amplitudes of the original signal

2) get power. this is square of amplitude as I was told. We can get this by:

signal_transformed = fft(original_signal);
normalized_power_spectrum = signal_transformed .*conj(signal_transformed )/(length(original_signal)*length(original_signal));

Clear, why we might need the first point. But why we should observe the second? What's the pivotal point of the act there and what is spectrum power, why we rather study that than amplitude?

Thank you!