Most chemical reactions go pretty slowly at room temperature. This is good news most of the time, otherwise random parts of the environment would be exploding at regular intervals, but bad news for industrial processes which need reactions to occur. In order to speed them up, catalysts are used. A catalyst is any substance that speeds up a reaction without taking part in it so at the end of the reaction you have the same amount of catalyst as you started with.
Industrial catalysts are often metals, as most metals have a large number of electrons which are a little cavalier about exactly how close to the central atom they need to be. This allows the metals to use these electrons to help out in reactions before claiming them back once the reaction is over. Examples are iron-based catalysts used for making ammonia (the Haber-Bosch process) and the nickel catalysts used for making saturated fats.
Biological catalysts work on a very different principle. Rather than being metals with fast-and-loose electrons, biological catalysts are large complex molecules called enzymes, which contain specific pockets for the reactants to fit into. Once they are trapped inside the enzyme aids the reaction, either by forming temporary bonds with the reactants to help them fit together, or by simply holding them close enough to each other to actually react and form the product.
Most enzymes are found inside organic lifeforms, which means that they do not need high temperatures to function while metal catalysts tend to need a bit of an energy kick to get going. In fact enzymes will denature, or break, if heated up too far beyond their optimum temperature (for most around 40 degrees, although some bacterial enzymes can work at 100 degrees). In some cases, such as in biological washing powders, this can be a huge benefit as it means less energy is needed for the reaction and the clothes can be washed at lower temperatures. In some industrial processes, however, high temperatures are needed to increase the rate of reaction so cooling everything down to 40 degrees is impractical.
Another important point about enzymes is that unlike the metal catalysts they are incredibly specific. As the reactants fit into pockets inside the enzyme each enzyme can only fit the molecules it's meant to be catalysing. And as enzymes are large and complex molecules it's not so simple to just design them to fit the reactants you need. Again, this is fine for biological washing powders, as there are plenty of enzymes that have evolved to break down egg stains, blood stains, and form strange little bobbles on jumpers. For chemical processes it can be a bit more difficult - not many organisms have evolved to remove the toxic gases from petrol, or synthesise sulfur dioxide.
There is some work being done designing enzymes for specific purposes, to hopefully increase the number of reactions that can be catalysed by biological means. It's not the easiest job in the world though, as enzymes are made up of massive protein chains folded in strange and interesting ways and tweaking one part of them can have unforeseen repercussions on the whole molecule. It's an exciting area of research though, with implications for industrial and medical research as well as the academic.
Credit link for image 2.