Spectral images - How do they appear during ADC?
One way to represent AD conversion mathematically is to think of it as a multiplication of the signal by an impulse train, which is a sequence of dirac delta distributions spaced by the sampling period $T_s$.

With this in mind and remembering that multiplicating in the time domain is equivalent to doing convolution in the frequency domain, it's possible to see that the frequency representation of the digitalized signal will be the convolution of the frequency representation of the sampled analog signal with the frequency representation of the impulse train. 

As it turns out, the frequency representation of an impulse train spaced by $T_s$ is an impulse train spaced by the sampling frequency $f_s$. Also, the convolution of a dirac delta with any function $g$ is just $g$ itself. By displacing the delta function by $f_s$, we also displace the result of the convolution by $f_s$.

So, the spectrum of the digitalized signal will be an infinite sum of copies of the spectrum of the analog signal distant of each other by $f_s$. Since the spectrum is bilateral, if your analog signal has frequency components above $f_s/2$, those components will end up summed from two different replicas in the spectrum of the digital signal, and this is in fact the aliasing effect.