The name geologists give to the last 65 million years of geologic history. The era is often called the Age of Mammals since they became the Earth's dominant megafauna, and mammalian fossils are the traditional indicators for dating Cenozoic rocks.

In the 1760s, Italian geologist Giovanni Arduino created the first crude divisions of stratigraphic history. Without any real tool for dating layers (not even dating by fossils had been invented yet), he gave the names "Primitive", "Secondary", and "Tertiary" based upon the minerals contained in Tuscan rocks, and the apparent order of their deposition. Only "Tertiary" survives to this day: Through the years, other geologists refined the system, and calculated the amount of time each period took. The Primary Period covered most of geological time (what we now call the Precambrian), and the Secondary covered most of the rest (the Devonian through the end of the Cretaceous; a "transitional" layer discovered later in Britain would later become the Cambrian, Ordovician, and Silurian Periods).

In 1829, Jules Desnoyers extended the system, suggesting the term Quaternary for the uppermost layers of sediment. In 1833, Scottish geologist Charles Lyell based his division of the Tertiary and Quaternary periods upon the fossils he found in Paris Basin rocks. His divisions are gone now but many of the names survive, based upon variations of the Greek for "recent". In 1841, John Phillips, inspired by Adam Sedgwick's 1838 naming of the Paleozoic Era, coined the terms "Mesozoic" and "Cenozoic" to describe the eras afterwards. In 1866, Georg A.C.F. Naumann grouped the Paleocene, Eocene, and Oligocene epochs into the "Paleogene"; in 1869, Rudolf Hoernes grouped the rest into the "Neogene". These divisons are more sensible, but have not been widely adopted.

Tertiary Period:

Paleocene ("ancient recent") Epoch 65 - 54.8 mya
Named by Philipp Schrimper in 1874. As the biosphere recovered from the probable asteroid impact that wiped out the dinosaurs, mammals began to spread into the ecological niches left open. Rodentia and Insectivora existed but the predominant groups (Multituberculata, Mesonychia, and Dinocerata) all are extinct today. However, by the end of the Paleocene, large herbivorous mammals had evolved, and clear divisions of marsupials, carnivores, ungulates, and early primates can be identified. South America broke from Antarctica and Australia, and its own unique life (such as Xenarthra) developed. North America rifted from Europe, and a volcanic arc created an island chain that divided the Tethys Sea down the middle.
Eocene ("dawn of the recent") Epoch 54.8 - 33.7 mya
Perissodactyla and Artiodactyla became widespread. Australia separated from Antarctica, isolating the former with its marsupials. Cuba rifted from the Caribbean Plate but soon bumped up against North America. Antarctica slid over the South Pole, allowing a huge ice sheet to develop as a consequence of a new circumpolar current. Global temperatures and sea levels dropped, causing new erosion of the Eastern seaboard peneplain, revealing ancient rocks as the Appalachian Mountains. As the Farallon and Kula plates continued to subduct beneath the Americas, The Laramide Orogeny continued, forcing the Rocky Mountains up further and stretching out the Basin and Range region. Early leaf-browsing horses and other mammals crossed a land bridge connecting North America to Europe. The volcanic arc dividing the Tethys Sea solidified into a belt that now stretches from Bulgaria to Afghanistan; the northern section is now called the Paratethys Sea. The Mediterranean Sea was cut off from the Tethys Sea at its eastern end. In the foreland basin sea separating Asia from the rapidly-approaching India, the first primitive Cetacea evolved.
Oligocene ("slightly recent") Epoch 33.7 - 23.8 mya
Named by Hienrich von Beyrich in 1854. India finished colliding with Asia, strengthening the global cooling effect. The Earth continued to cool, sea level continued to drop, and what we would call "tropical" flora and fauna became restricted to what we would call the "tropics". About a dozen orders of mammals vanished completely. Such a mass extinction provided new opportunities for species that could adapt: ungulates spread into Europe, Carnivora began to become widespread. Most recognizably modern forms of flowering plants had evolved.
Miocene ("moderately recent") Epoch 23.8 - 5.3mya
The East Pacific Rise finally reached the Americas, and the Farallon Plate broke into the Juan de Fuca, Cocos, and Nazca Plates. Subduction of the Nazca Plate beneath South America caused the Andes to form. Baja California was rifted from the North American Plate and became stuck to the Pacific Plate. Florida rose from the sea. Arabia collided with Iran, raising the Zagros Mountains and making the Persian Gulf the last remnant of the Tethys Ocean. The Paratethys sea basin was broken into the remnants that would become the Black sea, Caspian Sea, and Aral Sea. The Alpine Orogeny finished, creating the Alps and Atlas Mountains; the western end of the Mediterranean Sea closed up for awhile and it dried up, locking up large amounts of salt and making global climates unstable.
Pliocene ("very recent") Epoch 5.3 - 1.8 mya
The Cocos Plate began to subduct beneath the Caribbean Plate, causing North and South America to join. Many species moved between the two continents, so that North America now has armadillos and opossums and South America has ocelots. A large number of South American marsupial species, especially the carnivores, were forced into extinction. India pushed the Himalayas up higher, increasing the cooling effect. There were still forests (Nothofagus) on Antarctica, but grasslands replaced forests in large areas of the world. In Africa, a particular group of primates (Australopithecus) learned to walk upright as an adaptation to living in the new grasslands.

Quaternary Period (still part of the Neogene):

Pleistocene ("most recent") Epoch 1.8mya - 11,000 years ago
Named by Lyell in 1839. The global cooling forces of the previous 30 million years culminated in several Ice Ages that dominated the epoch. Hominid species developed into modern humans, who spread to all corners of the Earth except for the Pacific islands. A large number of species evolved to giant size as an adaptation, but the woolly mammoth, the sabretooth tiger, and giant ground sloths were extinct by the end of the epoch. Elephants and horses disappeared from the Americas. Disease, inability to adapt to climate, and hunting by humans have all been proposed as explanations, but none has been thoroughly proven.
Holocene ("completely recent") or Recent Epoch 11,000 years ago - Present
This period is a human conceit, covering the period of human agriculture, settlement, and written history since the end of the last Ice Age. Sediments from this time consist largely of alluvium, but a rise in sea level as well as several catastrophic events (flooding of the Black Sea basin, the draining of Lake Agassiz and Lake Bonneville, as well as Lake Missoula forming the Channeled Scablands) made large changes to the landscape.

A few sources:

"Geowords", Hugh Rance's Geological Website - Cenozoic epochs

University of California, Berkeley Museum of Paleontology - Introduction to the Cenozoic

Ocean Oasis Field Guide: How Baja California and the Sea of Cortes formed

Palæos: Cenozoic Era