The term jitter describes the deviation of a signal's true sampling interval from its ideal.
If you digitize an analog signal at a sampling rate of 44.1kHz, you will take 44,100 samples per second of the signal's state at that sample's precise point in time. Which means that you would ideally take one sample every 22.675737 microseconds.
In the real world, the sampling interval will deviate from that ideal. Some of your samples will occur a few tenths of a microsecond before that ideal interval, others a few tenths of a microsecond after.
When these samples get saved to your storage medium, they will be written as a continuous stream of values, but without any information as to their actual timing, and/or deviation thereof. And when that stream of your previously stored samples is played back, it will simply be assumed that they should be played back at a constant rate of 44,100 values per second, equally spaced at the same 22.675737 microseconds that they were recorded at.
To understand what role jitter plays during recording, imagine the following:
Imagine a perfectly smooth sine wave drawn on a sheet of graph paper.
Write down the Y-value of the sine wave at every point where it crosses a vertical line on your graph paper.
Now draw a dot for each of the values you've just written down, precisely on the same vertical line that you took the value from, at the appropriate Y-position an inch or so below your original sign wave.
Once you're done, you should end up with a very close approximation of your original sine wave. You have just recorded and played back a jitter-free signal.
Now repeat the above, but instead of writing down the Y-value of the sine wave at every point where it crosses a vertical line on your graph paper, measure each and every value slightly before or slightly after that vertical line on your graph paper, alternating between "slightly too early" and "slightly too late" at random.
Now draw a dot for each of the values you've just written down, again precisely on the same vertical line that you (sort of) took the value from, at the appropriate Y-position an inch or so below your original sine wave.
Once you're done, you should end up with a still somewhat close approximation of your original sine wave — but instead of a continuously smooth sine wave, you will now have something that looks a bit bumpy. You have just recorded a jittered signal, and played it back jitter-free.
The inverse is true as well. Measure your sine wave precisely on the vertical lines, but draw each value slightly before or after that vertical line at randomly changing deviations, and you will, again, end up with a somewhat bumpy representation of your original signal. You are looking at a jittery playback of your perfectly sampled original signal.
In the real world, both happens. So not only do you not have a perfectly regular sampling interval, you also don't have a perfectly regular playback. The trick is to minimize those deviations from the ideal interval on both ends, but you will never be able to get rid of it entirely.
There's also no way to compensate for this or correct the jitter after the fact, simply because the samples in your recording don't contain any information as to when exactly each sample was taken.
You could, of course, "invent" a new recording format that not only stores the sampled values themselves, but also a precise timestamp for each and every sample to the most precise degree that your hardware allows. But that wouldn't solve your problem either, as that time stamp would be informed by the same clock signal as your analog to digital converter; the timestamp values would very likely be just as inaccurate as your sample timings.You will probably make things even worse, since the timestamp is likely to be even less precise (because it's more involved to determine) than your actual samples were to begin with, adding deviations onto deviations.
The easiest way around this is to just use hardware during recording and playback that has a good enough internal clock to stay as close to the ideal interval as physics allows. Which is also why many of your Schiit DACs do a relay click when the sampling rate changes from one track to the next: They have dedicated clocking circuits for each, 44.1 and 48kHz, and their multiples — and whenever you hear that click, your DAC switches from one of them to another one.
And for what it's worth: Jitter doesn't matter at all during storage or during any asynchronous transmission of a digital audio signal, as the values will be buffered before playback, and the playback is controlled by its own clock. The quality of that clock matters, obviously, and so does the jitter within a synchronous digital audio signal where the signal itself directly informs the clock for playback, as is often the case in S/PDIF, for example.
