In addition to the useful answers already given where the variable settings can be used, one specific situation not yet mentioned when you must use the variable VOLTS/DIV
setting on an analog 'scope, is when measuring the rise or fall-times of a waveform.
The rise or fall-time of a waveform is usually measured between the 10% and 90% amplitude points of the waveform, irrespective of the actual voltage. In other words, the absolute voltage is not relevant for this measurement, because this is a measurement of time.
The 'scope display graticule (grid) will have 0%, 10%, 90% and 100% horizontal lines, for example:

(source)
The VERT POSITION
control is used so that the initial signal level
(this is usually, but not always, the minimum level) is aligned with
the 0% line.
Then the VOLTS/DIV
switch and its variable control are adjusted,
so that the final signal level is aligned with the 100% line (this
is usually, but not always, the maximum / peak waveform voltage level).
Notice that because we are not measuring the voltage, it does not
matter that the vertical amplifier is now likely to be in an
uncalibrated state (since the variable adjustment likely needed to be
moved from the CAL
position, to make the waveform's final signal level
align with the 100% graticule line).
The TIME/DIV
switch should be set to the fastest setting, which
still allows the complete rise or fall (whichever is being measured)
of the waveform to be seen. However this variable control must be
set at the CAL
position, since we are measuring time.
Then use the HORIZ POSITION
control to move the whole waveform
horizontally, to make measuring the rise or fall-time easier e.g.
align the waveform rise at 10% (or fall at 90%) to a "major
division" vertical graticule line. Then it is easier to measure the
number of divisions (i.e. the time) of the rise/fall of the waveform,
knowing the TIME/DIV
(timebase) setting.
In summary:
- If you are measuring voltage then
VOLTS/DIV
variable control must be set to CAL
; however you can use the TIME/DIV
variable control if you are not also measuring time, and if that adjustment will make your work easier in any way e.g. make it easier for you to see a specific part of the waveform.
- If you are measuring time then
TIME/DIV
variable control must be set to CAL
; however you can use the VOLTS/DIV
variable control if you are not also measuring voltage, and if that adjustment will make your work easier in any way e.g. make it easier for you to see a specific part of the waveform.
Some other examples of using an analog 'scope are described in this "Using Oscilloscopes" webpage.
[The names of the 'scope controls can vary slightly between manufacturers, but I have tried to use common names.]