Although everyone might believe that they can define what "catalysis" or a catalyst is, it is really hard to find the correct definition for these terms. Simply and in general, a catalyst is a molecule/ion/element/heat/light etc. that lowers the activation energy of a chemical reaction. So, the reaction will go faster and in the end you'll end up regenerating your catalyst. A simple diagram is shown below.
The term catalysis was first introduced to chemistry by Berzelius. The paper I am sharing here is a really nice review on catalysis. In case you are wondering, there is not much "chemistry" in the paper. This is more like a history of science article that divided catalysis into five different periods and lists the major events and scientists chronologically. The five periods according to the authors are : production of alcohol by fermentation, "systematic research and the discovery of new catalytic processes," "industrial applications," synthetic fuel production, synthetic polymers. Of course I do not agree with these general and broad periods. But, as I said this is a really nice paper that gives you enough information on the history of catalysis.
Catalysis is one of the greatest areas of research in chemistry. We know that enzymes easily catalyze several reactions at physiological conditions. But, when it comes to test tubes, reactors etc., this is not the case. So, discovering (or synthesizing) the right catalyst is not an easy task. It should also be relatively inexpensive and unique so that it stands out among the other catalyst candidates.
It is free to read and I hope you enjoy the article: