The term comes from the cornucopia, the "horn of plenty" of Greek mythology, which magically supplied its owners with endless food and drink. The cornucopians are sometimes known as "Boomsters", and their philosophic opponents—Malthus and his school—are called "Doomsters" or "Doomers."
Stereotypically, a cornucopian is someone who posits that there are few intractable natural limits to growth and believes the world can provide a practically limitless abundance of natural resources. The label 'cornucopian' is rarely self-applied, and is most commonly used derogatorily by those who believe that the target is overly optimistic about the resources that will be available in the future.
One common example of this labeling is by those who are skeptical of the view that technology can solve, or overcome, the problem of an exponentially-increasing human population living off a finite base of natural resources. So-called cornucopians might counter that human population growth has slowed dramatically, and not only is currently growing at a linear rate, but is projected to peak and start declining later this century.
In practice, the cornucopian view relies upon the economic law of supply and demand, which has the following implication: as long as the price of a good is free to adjust, all consumers who wish to purchase the good at the going price are able to do so. Resources do not run out, they simply become more expensive.
In the Peak Oil debate, the views of those labeled as cornucopian are very diverse, ranging from the simplistic "we will never run out of oil" to pessimistic views such as "we might transition to alternatives fast enough to barely avoid the collapse of civilization". The spectrum is broad enough that some who are characterized as cornucopians by doomers might be characterized as peakniks or even doomers by other cornucopians. A typical cornucopian view might be characterized as "there exist viable solutions to the problem of peak oil".