Sampling is the process of converting a continious time signal into a discrete time signal by measuring the signal at periodic instants in time.
If the number of samples per seconds increases the sampled signal will approximate the continuous signal more closely. However, if the sampling rate is high enough the sampled signal will contain all information to reconstruct the original signal. The Nyquist sampling theorem states that a signal may be perfectly reconstructed if it is sampled at a rate greater than or equal to twice the frequency of the highest frequency component of the signal.
Sampling is the first step in the digitalization of a analogue signal. After sampling, the samples have to be quantisized.