Your question is actually a three-part question in disguise, of which I cannot answer all parts, but let me tell you what I do know.
Part 1: What causes variations in vertical position within the context of the refered sentence?
If you read that section more carefully it is not so much variation of the seabed depth, but variation in the measurement of the seabed depth. Using known fixed structures on the seabed they found out that different runs give a different vertical position of these structures. Let me expand your quote:
[...] Repeated sampling of stable immobile seabed structures (fishing drag-board traces, ship wrecks) indicates that the reconstructed overall vertical position with respect to a fixed chart datum may vary by more than 10 cm from survey to survey. The causes of this variation have not been resolved yet. Hence, without a vertical reference present within the surveyed area overall variations in the seabed of less than 20 cm cannot be derived unambiguously over periods longer than several months. In contrast, using a fixed seabed structure as vertical reference the precision of multibeam data can be less then half a meter in the horizontal and one centimetre in the vertical [...]
This means that in situations without stable vertical references measurements at different times cannot be compared easily, and simply subtracting the bed heights would not necessarily give the change in bed height over the elapsed time.
However, when there are stable structures, such as a ship's wreck, you can use the difference in the measurements of the vertical position of that structure to correct measurements of the entire seabed, giving a much better vertical precision.
Part 2: What causes variations in the measurements between measurement runs?
The section referenced mentions that the exact causes of the different measurements have not been resolved. Most likely it is a combination of inaccuracies of the used instruments, on which I'm definitely not an expert, and I'm not even sure this is the right Stack Exchange to ask that question.
Part 3: What causes true variations in the absolute seabed height?
This is an entire field of research on its own, called coastal morphodynamics, which is too broad to be answered in a single Stack Exchange answer. Without a specific question you wouldn't get a more sensible answer than it a depends on the seabed composition and water flow.