Activation energy and the rate at which occurs (chemical kinetics) are inversely related. While activation energy is not the only factor that influences reaction rates, it is generally true that increasing the activation energy of a given reaction slows it down, and that lowering the activation energy of a reaction speeds it up.
Activation energy, for those unfamiliar (or needing a refresher) with the term, is the net energy required before a reaction to occur. If you are looking at a reaction diagram, it will be the difference in energy between the ground state(s) of the reactants and the highest energy state during the reaction. (A multi-step reaction has multiple activation energies throughout, but the step with the largest activation energy will be the rate-determining step.)
Activation energy may come from any number of sources, though heat is probably the most common. Light, acoustic energy (sound waves), and collisions are other energy sources that may initiate a reaction. Whatever the form, if insufficient energy is present to overcome the activation energy barrier, the reaction comes to a stop. In a spontaneous reaction, a single occurrence of the reaction provides enough energy to meet the activation energy requirements for more reactants to undergo the reaction. These are frequently the dramatic, uncontrolled reactions that people fear, such as explosions.
Explosives are excellent examples when discussing activation energies. Some explosives have high activation energies and can be transported, molded, and even tossed about with reasonable safety. (Think of plastic explosives.) Because they have a high activation energy, it takes a significant energy input (like an electric discharge) to set them off. Once begun, the reaction is spontaneous - but only once the original, large amount of activation energy is supplied. On the opposite end of the spectrum, there are explosives like nitroglycerin, which has such an extremely low activation energy that a mere vibration can supply the necessary energy. This too, results in a spontaneous reaction, so the end result is really no different, only the path in getting there.
Many reactions occur in solution, and are more often of interest than explosives. (They have a wider variety of reaction rates for one, and are much easier to clean up for another.) Keep in mind that most of the chemistry in the human body is also done in solution, so this is applicable to biology as well. When activation energy is high, reactions often proceed too slowly to be useful. To speed them up, chemists (or cells) use catalysts to help the reaction along by lowering the activation energy of the rate-limiting step in the reaction. A catalyst can work in a variety of ways, possibly providing a necessary hydrogen bond, weakening a bond that must be broken, orienting the reactants in the proper position to react with one another, or various other interactions. Metals like platinum, palladium and gold are often used as catalytic surfaces by chemists. Cells use large protein structures (they're called enzymes - but they are merely biological catalysts) which sometimes contain a metal center (like iron) but do the same jobs regardless. In either case, lowering the activation energy has the same effect - the reaction rate increases.