What is meant by a reversible reaction

It's exactly what it says, the reagents can react to form the products, and the products can react to form the reagents.

All reactions, in theory, are reversible. They keep reacting until the reaction meets an equilibrium state (where they are still reacting, but the proportion of reagents and products stay the same because the rate of reaction in each direction is the same).

You can see how equilibriums are affected by studying Le Chatelier's principle.