In simplest terms, the addition of catalyst lowers the activation energy of the reaction.
The activation energy can be thought of as the energy barrier that must be overcome for the reaction to take place. Or, it is the difference in the energy of reactants and the maximum energy in the reaction-energy curve. The catalyst provides an alternate reaction pathway, with a lower activation energy, and hence speed up the reaction. One of the mechanism for this is the presence of more favorable sites of reaction (something akin to a lock and key arrangement). Another mechanism is the break-down of the reaction into smaller sub-steps, each with high reaction rate.
Therefore, it can be safely said that an appropriate catalyst will bring down the activation energy from 20 kJ required in an uncatalyzed reaction.
A chemical reaction typically happens in a series of steps. Each step, called an elementary step, requires a certain amount of activation energy to begin breaking bonds between reactant particles, and it has a certain rate or speed. Each step (except the last one) has a reaction intermediate that is temporarily produced before it changes in a later step.
The potential energy of the reaction intermediate is related to the activation energy of that step, i.e., the higher the potential energy of the reaction intermediate, the higher the activation energy. And as the activation energy increases, generally speaking, the reaction rate (speed) decreases. This is because fewer reactant particles have sufficient energy to create the high energy intermediate.
A catalyst changes the steps by changing the reaction intermediate, which has a lower potential energy than the non-catalyzed reaction. Since the potential energy of the intermediate formed with a catalyst is lower, more reactant particles have sufficient energy to create this intermediate and the reaction proceeds faster, thereby increasing the rate.
For these reasons, the catalyzed reaction would have a lower activation energy than the non-catalyzed reaction, therefore the activation energy (energy to start) the catalyzed reaction will be less than 20 kJ.