Question: "How does the Cambrian Explosion fit within the framework of young-earth creationism?"
Answer: The earth's crust consists of many layers of fossil-bearing rock. It was once believed that the lowest layer of fossil-bearing rock was the Cambrian and that Precambrian rock was totally devoid of any fossil remains. It is now known that there are actually some, though very few, primitive fossils in the Precambrian. But it is not until the Cambrian layer that we find a sudden burst of life.
The “Cambrian Explosion” refers to the sudden appearance of most of the world's known animal phyla, all within a very brief period of geological time (by the conventional standard). The sudden appearance of so many of the major innovations to the basic structures of known animal forms has always been somewhat problematic for Darwin’s theory of gradual innovation. But how does the Cambrian Explosion fit with the framework of young-earth creationism?
The old-earth position is that the vast majority of earth's strata represent long epochs of time, typically millions of years, and that the fossils found in the lower layers evolved before those found in the upper layers. The young-earth position is that nearly all of the strata from the Cambrian period on up were deposited in relatively quick succession as the result of a catastrophic global deluge and subsequent natural disasters, and that the order in which fossils are found is a result of hydrological mechanics (hydrologic sorting for example, the phenomenon whereby dirt spontaneously settles into layers after being kicked up in water).
The conspicuous presence of so many of the world's known animal phyla in the bottom layer does not prove or disprove one position or the other. So young-earth proponents rely on other physical evidences to make their case, including poly-strata fossils (that is, fossils that pass through multiple strata), misplaced and missing fossils and strata, the lack of erosion between strata, the deficiency of bioturbation, undisturbed bedding planes, the limited extent of unconformities, soft-sediment deformation, and well-preserved surface features between layers, etc.
There are, for example, plenty of out-of-place fossils. Sometimes rock layers containing what are thought to be older fossils are found above rock layers that contain what are thought to be younger fossils (the younger fossils should be on top). The solution for Darwinian geologists is to argue that the strata containing the misplaced fossils were shuffled out of order by some natural geological process. They then reorganize the discrepant fossils and rock layers logically using the assumed order in which the creatures were supposed to have evolved; i.e., this organism was supposed to have evolved before this one, so it goes here on bottom, while this organism was supposed to have evolved after this one so it goes here on top, etc. Darwinian biologists then turn around and use the evolutionary progression organized by the geologists as evidence for the evolutionary progression that the geologists used to organize the strata. This is, of course, circular reasoning.
To summarize, each viewpoint, whether young-earth creationism, old-earth creationism, or Darwinian evolution, struggles somewhat with explaining the Cambrian Explosion. In no sense, though, is the Cambrian Explosion contradictory with young-earth creationism. In fact, young-earth creationism perhaps has the clearest explanation for the Cambrian Explosion, that of the global deluge. Whatever the case, the evidence for the Cambrian Explosion is no reason to doubt the veracity of Genesis’ account of creation (Genesis chapters 1-2, 6-8).