Posthuman is a term that refers to a hypothetical future being whose basic capacities so radically exceed those of present humans as to be no longer unambiguously human by our current standards. "Posthuman" does not denote just anything that happens to come after the human era, nor does it have anything to do with the "posthumous". In particular, it does not imply that there are no humans anymore.
Posthumans could be artificial intelligences, or they could be uploaded consciousnesses, or they could be the result of making many smaller but cumulatively profound augmentations to a biological human. The latter alternative would probably require either the redesign of the human organism using advanced nanotechnology or its radical enhancement using some combination of technologies such as genetic engineering, psychopharmacology, anti-aging therapies, neural interfaces, advanced information management tools, memory enhancing drugs, wearable computer, and cognitive techniques.
A posthumanist, on the other hand, is simply someone who advocates posthumanism.
"Posthuman" is also a song by the band Marilyn Manson, found on their 1998 glam rock release, Mechanical Animals. It is said by some to be inspired by the concept of posthuman described above.