I would say that the key points behind it can be explained in layman's terms.
I'm not too up on my evolution theory, though. Perhaps someone here can make a decent case for it.
Evolution is a change in the inherited traits of a population over time. This is a proven fact, laboratory research has proven this, on many occasions. For example, unicellular organisms have evolved the ability to use nylon and pentachlorophenol as their sole carbon sources. Lets integrate chemistry and history here, nylon was first produced on February 28 1935 by Wallace Carothers, single celled organisms have lived and evolved for billions of years, yet it evolved the ability to use a man made material as its sole carbon source. This is microevolution, evolution below the species level, which isnt controversial in marked contrast to macroevolution.
Okada, H., S. Negoro, et al. (1983) "Evolutionary adaptation of plasmid-encoded enzymes for degrading nylon oligomers." Nature 306: 203-206
Macroevolution on the other hand is very controversial because it details the transformation of one species to another, such as the common claim that humans come from monkeys, which offends most people, however macroevolution doesnt stop there. In any case, humans arent the descendents of monkey, chimpanzees, or gorillas, but rather humans share a common ancestor with the latter two. At one point, paleontologist believed Ramapithecus was our common ancestor, but advanced biochemical research proved that our common ancestor wasnt Ramapithecus, it biochemical research also proved that our common ancestor lived around 5 million years ago, rather then 25 or 15 million years go.
Sarich VM, Wilson AC. Immunological time scale for hominid evolution. Science 158, 1967, p. 1200-1203.
This same type of anti-evolutionary lunacy is obvious with humans, some academics argue that humans are all the same despite surface differences, which is untrue, forensic scientist who identify and classify humans into taxonomic categories can distinguish a human of black African descent from a human of white European descent by their non-living physical remains and the absence of skin color, they can determine their ancestry by their bones making a clear case that skin color isnt the only physical and genetic difference humans have and most certainly not one that would be used to classify them into biological categories.
http://www.pbs.org/wgbh/nova/first/gill.html