A catalyst is a substance which increases the rate of reaction without being chemically changed at the end of the reaction.
A reversible reaction is one where the forward reaction and the backward reaction happen simultaneously. For example:
3H₂ + N₂ ⇋ 2NH₃
In such a reaction a catalyst speeds up both the forward and the backward reactions. Hence, although the system will reach dynamic equilibrium more quickly, the addition of a catalyst will not affect the position of equilibrium.