Most of your ammonia and nitrites need to be processed biologically. These wastes cannot be filtered but need to be broken down. Some filters will colonize with bacteria which will do the job. However, if you have live rock this should do the job for you after your tank has cycled (which allows enough buildup of these bacteria to handle a normal tank's waste).
Nitrates will build up from the above processes. These can be removed with 1) a deep sand bed (which will have different bacteria- which break nitrates down to nitrogen, which bubbles away), 2) plant life (algae) or 3) water changes.
Carbon will have little effect on any of these wastes. There are many other compounds which carbon can remove.Evolution has provided marine life with many options for different species to survive. One of them is the development of toxins which prevent other life from living. Some of these will be waterborne. Carbon will remove these compounds and provide another level of security. However, most of these never build up to enough concentration to cause serious problems (particularly as the bacteria in your live rock will also tend to break down a fair amount of toxins also. Once the toxins start to build up, the bacteria that can use them for food break them down and multiply. Once this happens, they would only have a very local effect). The major disadvantage of carbon is that it has to be changed frequently otherwise the compounds just build up again. Many aquarists can't see a difference in their tanks with or without carbon. I see the major advantage would be for someone who is intentionally overstocking their aquarium or for treating a specific problem (like cloudy water).
