Neo-Darwinism is a "materialistic theory of origins" which states that "evolution is driven by random genetic mutations followed by the weeding out of unfavorable variations by natural selection."  The element "Neo-" in the term, meaning "new" refers to the melding of the Christian science of genetics put forward by Gregor Mendel with the liberal Darwinian pseudoscience of evolution.
The term evolution can have different meanings, such as “change over time” or even “progress.” However, in modern biology, evolution centers on two ideas. The first is that all the organisms we see are descended from a single common ancestor somewhere in the distant past. The second foundational idea is that an unguided process of natural selection (“survival of the fittest”) has the power to produce fundamentally new forms of life through random mutations. This view of evolution is known as “Neo- Darwinism.” 
Despite the fact that most Americans believe that God created life, the only “origin of life” theory taught in the majority of American schools is Neo-Darwinism, which at its core holds that a random undirected process has led from non-life to all of the marvelous complexity we see in the living world. [ibid]
“By coupling undirected, purposeless variation to the blind, uncaring process of natural selection, Darwin made theological or spiritual explanations of the life processes superfluous.” From Evolutionary Biology, a widely used college textbook.
Darwinian evolution argues that life arose from a primordial sea on a lifeless planet through a chance collision of chemicals, and that over billions of years, this biological accident gave rise to all of life, including humans.