Refers to chemical elements with an atomic number higher than that of uranium, i.e. Z > 92. Because these heavy elements tend to be highly radioactive, they generally do not occur in nature because they are very unstable and decay with a short half-life into lighter elements. Some examples of these elements include plutonium, americium, mendelevium, and rutherfordium.

These elements are often created by bombarding some stable element with sub-atomic particles, most often neutrons or perhaps the atomic nuclei of lighter elements. Neutrons are the most effective at producing transuranic elements, because they are neutral and are subject to the strong nuclear force. Most weapons-grade plutonium is produced by nuclear reactors that bombard Uranium-238 with neutrons. Neutron capture changes the U-238 into U-239, which decays in about 24 minutes to Neptunium-239, which then beta decays into Plutonium-239 2.3 days after. Atomic nuclei of light elements such as alpha particles have also been used to create elements with high atomic number.

A transuranic element is an element with a greater atomic number than uranium, atomic number 92, as it has the highest atomic number of any naturally occurring element.

The first of these elements was neptunium, produced at the University of California at Berkeley in 1940 by E. M. McMillam and P.H. Abelson. An isotope of element 93, neutrons bombarding uranium-238 produced uranium-239 and after a few days of beta decay neptunium-239 was formed.

238U + 1 --> 239U

239U --> 239Np + 0

Plutonium, atomic number 94, was next. A cyclotron accelerated deuterons and were slammed into uranium to produce neptunium-238 which later decayed to plutonium-238. This isn't what most people think of as plutonium today which is used in weapons and reactors, which is plutonium-239

238U + 2H --> 238Np + 21n

238Np --> 238Pu + 0e

Americium (atomic number 95) and curium (atomic number 96) helped scientists understand how elements after actinium should fit into the periodic table. Originally it was thought that these elements belonged under the d-transition elements after actinium and uranium ended up in Group VIB under tungsten. Glenn T. Seaborg thought perhaps a second series of elements belonged under the periodic table and they were named the actinides. This helped scientists separate these later elements due to their expected chemical properties which could be determined by their plane in the table.

Other than the best known uses, weapons and reactors, these elements are often used commercially. Since plutonium-238 only produces weak alpha radiation it is used as a power source for things like satellites and pacemakers. Gamma rays from Americium-241 are used to measure the thickness of metal sheets and their alpha particles are present in home smoke detectors to determine is there is smoke in the air.

Sources:
Ebbing, Darrell D. and Gammon, Steven D. General Chemistry - Seventh Edition. Boston: Houghton Mifflin Company, 2002.