Most DSP applications deal with analogue signals.
The analogue signal - a continuous variable defined with infinite precision - is converted to a discrete sequence of measured values which are represented digitally.
Information is lost in converting from analogue to digital, due to:
These effects are called quantisation errors.
The continuous analogue signal has to be held before it can be sampled.
Otherwise, the signal would be changing during the measurement.
Only after it has been held can the signal be measured, and the measurement converted to a digital value.
The sampling results in a discrete set of digital numbers that represent measurements of the signal - usually taken at equal intervals of time.
Note that the sampling takes place after the hold. This means that we can sometimes use a slower Analogue to Digital Converter (ADC) than might seem required at first sight. The hold circuit must act fast - fast enough that the signal is not changing during the time the circuit is acquiring the signal value - but the ADC has all the time that the signal is held to make its conversion.
We don't know what we don't measure.
In the process of measuring the signal, some information is lost.
Sometimes we may have some a priori knowledge of the signal, or be able to make some assumptions that will let us reconstruct the lost information.