Organic chemists study the compounds that contain the element carbon as a key ingredient. This may seem limiting, but over 90% of all known compounds have at least some carbon in them. All the foods we eat, most over-the-counter and prescription medicines, plastics, wood, paper, paints, our clothing, much of our cars, even our own bodies themselves are all made of carbon. Some organic chemists study how to make new carbon-based molecules with new, more desirable properties (a flexible plastic that can conduct electricity, a more effective version of aspirin) while others do more C.S.I.-type work, figuring out the identity of an unknown chemical (say, one extracted from tree sap that shows promise as a new anti-cancer drug) or even looking for cures for heart disease in spider venom or other equally unlikely places. Organic chemistry is a chance to do science while working on projects that have the potential to help raise the standard of living or even save lives on a grand scale.
One bit of organic chemistry which has been in the news lately is "Nanotechnology" which is really just using organic molecules to build tiny mechanical devices. Chemists can make gears, wheels, and other items which we hope can ultimately be assembled into small machines that can perform sub-microscopic tasks.
Professional opportunities for organic chemists are highly varied; these chemists work for pharmaceutical companies such as Hoffman-LaRoche, DuPont and other plastics firms, petrochemical concerns such as Exxon-Mobil, agrochemical firms like Monsanto, paint and coatings manufacturers such as Sherwin Williams, and food-based companied such as Tropicana®. If you feel inclined to start your own course of research you can do so at any one of a huge number of colleges or universities where you can plan your studies and carry them out however you please.