In the picture above S marks the duration for sample and hold which indicates that in this time period the input signal will actually captured that is a snapshot if its physical value is taken.
After this time it will be converted to a digital value in the conversion phase marked with C.
When the conversion had finished this loop may start again. In parallel the result could be used for further processing marked as R.
This technique has a natural boundary in terms of how fast it can provide new samples which is the sum of the sample time and the conversion time.
Thus limiting the highest frequency of the samples signal according to the sampling theorem of Nyquist-Shannon.
To overcome this limitation a different technique of sampling named ETS [comp. [2] p.273ff] can be used although it introduces limitations on the applicability.
The principle of ETS is shown in chapter xy of this wiki.