Discrete-time system: getting the true frequency from normalized frequency
The maximum frequency of a discrete-time signal is half the sampling frequency. A signal with maximum frequency in discrete time is an alternating sequence, and since its period is two sample intervals, its frequency is $f_s/2$. All frequencies in the discrete domain are normalized by that maximum frequency. 

This implies that a discrete-time system's behavior can be described independently of the sampling frequency. E.g., if you have a low pass filter, the cut-off frequency is fixed in terms of relative frequency. The actual cut-off frequency in Hertz depends on the sampling frequency.

Often you will encounter the normalized frequency in radians:

$$\omega=2\pi\frac{f}{f_s}\tag{1}$$

where $f_s$ is the sampling frequency, and $f$ is the frequency in Hertz. Note that the frequency response of a discrete-time system is $2\pi$-periodic with respect to $\omega$, i.e., with respect to $f$ it is periodic with period $f_s$.