This was my brother’s explanation when I asked the same question. It was so good, I felt like I needed to share it to help other people. The following are his words to me:
Let's start with fluids. Anything that flows can be modeled as a fluid. Air, water, blood, oil, etc.
All fluids have viscosity, meaning they are sticky, and stick to surfaces.
Oil sticks to your hand. So does water, and air as well. Air also sticks to a wing or turbine blade surface. The viscosity of a fluid is independent of the speed of its flow, and more to do with its chemical makeup.
The Reynolds Number (Re) is proportional to the ratio between the momentum of a flowing fluid and its viscosity. The lower Re, the more viscosity governs the flow behavior, so the more it sticks to a surface, and the flow is laminar. The higher the Re, the more its velocity governs, so the less it sticks to surface, and the flow is turbulent. Laminar flow is straight lines. Turbulent flow is eddies and swirling vortexes.
Re is a function of density, velocity, viscosity, as well as the distance along the surface it has travelled. In the case of an airfoil, distance travelled simply means the distance from the leading edge that the flow has reached. Re has a different value at each location aft of the leading edge. At the leading edge, Re is 0 since the distance is 0.
For any airfoil, Re starts at 0 at the leading edge, and starts to increase as the flow moves aft. At some point the Re is large enough that the flow goes from laminar to turbulent.
The idea with small scale aerodynamics vs. large scale is that since the dimensions and the speed of a paper airplane (for example) are so much smaller than that of a B747 or a Cessna, that the Re range is much smaller. Smaller Re range means that viscosity governs for more of that range, and hence there is more aerodynamic drag for the amount of lift generated.
There is another concept called the boundary layer that I've left out, but you should understand it.
See these for more explanation:
* http://www.paperplane.org/Aerody... (section "Low Reynolds number flight")
* https://en.wikipedia.org/wiki/Re... (the first paragraph)
This answer can be viewed on Quora: quora.com/What-is-meant-by-the-Reynolds-number