Guys, please, if you really only do have a marginal understanding,
don't post or at least mark it as such. Explaining in entirety what
the Reynolds numbers means will fill one or two chapters in a good
aerodynamics textbook.

What Cavelamb wrote is good, what Jim wrote is, as he said, marginal
understanding, but not wrong, but what Gerry wrote is between
borderline and wrong.

I will try and summarize a bit (but after 7 years of university, it's
probably pretty theoretical):

The Reynolds number is determined as

Re = v * L / nu

v is the speed of the airflow,
L is the "characteristic length" (I'll get into that)
nu is the "cinematic viscosity" (dynamic viscosity divided by density,
which yields roughly 1.5 * 10^-5 m^2/s at ISA MSL conditions - no
fudge factors such as "9346" when using SI. The density effects Gerry
wrote about are 99% due to the impact of density on the dynamic
pressure, and not on Re - and the dynamic viscosity of air and water
are much different to begin with)

Physically speaking, it gives you the relation between viscous and
inertial forces in a fluid (as has been said). Which won't really tell
you anything in the beginning. Very roughly it means whether the
airflow will be laminar or turbulent (see last post by Cavelamb).

This means you can get an infinite number of Re on an airplane, just
as has been written. It cannot (really) be chosen, but is determined
by size and operating conditions of the airplane.

On an airfoil, the characteristic length L is the chord. Wind tunnel
measurements on airfoils are done at certain Re. So if you know your
airflow speed and chord, you can get the right polar to figure out how
your airfoil will behave. Re mostly has an effect on the length of
laminar airflow (transition usually occurs at a certain Re, which is
then not calculated with L, but rather with x, meaning the length of
surface the air has travelled on the airfoil up to this point) and
hence drag, and since laminar and turbulent flow behave differently
with regard to flow separation (check for pictures on Google what this
means), it also has an effect on the maximum lift coefficient the
airfoil will achieve.
In general, higher Re lead to lower drag coefficients and higher max
lift coefficients, but a smaller "laminar bucket", which means the
range of lift coefficients the airfoil can operate in to achieve low
drag is smaller (especially interesting for sailplane and other low-
drag applications).

In short, you need it if you (seriously) want to design an airplane
and estimate its performance.

But the difference between wind tunnel testing and reality is much
greater than the difference between Re = 1 * 10^6 and 2 * 10^6, so it
doesn't really matter for homebuilders. It can become interesting for
builders of high-performance model airplanes and of course
aerodynamically challenging tasks such as designing sailplanes.

Oliver