A digital signal is commonly described as a signal which is discrete both in time and value/amplitude/magnitude.
I understand what is "discrete in time" (say, the signal is received each 1 second instead of continuously/sequentially or all the time), but I don't understand what is the meaning of the signal being discrete in value/amplitude/magnitude.
What is the simplest example from daily life, or even from a laboratory, for a signal being discrete in value/amplitude/magnitude?
A specific example, and common application where this occurs is with an "Analog to Digital Converter" (A/D), which is the boundary between the analog and digital world. Computers store values with a finite number of bits to represent values which is a primary motivation for such "digital signals". It is well understood what the implications are in terms of how many bits to sample a continuous time signal and at what rate to properly capture the signal to not exceed a specified level of distortion, both in how many bits to use setting the precision of the vertical axis, and what sampling rate to use setting the step size along the horizontal axis. This can later be converted back to a discrete time signal using a "Digital to Analog Converter" (D/A).
See the plot below showing the conversion of an analog sine wave to a digital signal, where the signal becomes discrete in time which is "Sampling" along the horizontal time axis, and discrete in amplitude which is referred to as "Quantization" along the vertical amplitude axis.
Another very simple example of discrete in magnitude is making measurements with a ruler and recording the measurements to the closest precision mark given on the ruler, such as 1/16" increments for inches as given in the graphic below.
And finally another example from daily life of discrete in value is the answer you typically get when you ask someone how old they are, which is a most often given as a value rounded to the closest integer. However noted as given by the ruler example, values need not be restricted to integers to be discrete, but would generally be a ratio of integers- such as $m/16$ for any positive integer $m$ in the ruler example.
The two major systems for discrete values for purposes of storing and manipulating values in a computer are "fixed point" and "floating point".
