First off, just to be clear, it's spelled "entropy." No biggie.
Anyway, as you've probably read, all reactions seek the maximum entropy possible. So, when a reversible reaction proceeds, it will only go far enough to reach maximum entropy and then the forward and reverse reactions will be progressing at the same speed, equilibrium.
However, truly reversible reactions are not possible. You could theoretically have a reaction with zero entropy change, but in real life this doesn't happen. Therefore, a "reversible" reaction in the truest sense is not possible. If a reaction WERE truly reversible, products and reactants would exhibit equal amounts of entropy so they could interchange freely. The statement "entropy of a reversible reaction is zero" is an idealized scenario to illustrate an idea, but doesn't actually happen.
It might be easy to think of it this way: In the case of equilibrium, you're measuring a value of entropy, but in the case of a truly reversible reaction, you're measuring the change in entropy between products and reactants (and every step along the way, I believe. The change would be zero at every point or it would also reach an equilibrium and stop.).
I really feel like I didn't explain that too well, but hopefully it helped in some small way.