My imperfect understanding:
As bodies get smaller, the frictional effects as they move through fluids becomes increasingly more significant in affecting the interaction between the bodies & the fluids.
For a example, to a microscopic animal (say a flagellate or similar), moving through water would seem more as if it was trying to force its way through treacle.
A reynold's number is a way of accounting for the proportional differences caused by changes in size & speed. Once the proportional effect is known then it can be factored for when extrapolating the effects seen in one body, compared to a different body eg a model of an aircraft vs the real full size aircraft.
Genghis, where are you when I need you?