About one-tenth of the first write-up* above is fact; the rest is
rubbish. Before 1950 or thereabouts it could have had some place in a
scientific discussion. The persistence of this
ignorance today is very disturbing.
There was abundant complex life before the Cambrian explosion, of many different kinds, including animals. There is no good evidence that the present phyla that became widespread in the Explosion actually originated in it.
The basic fact is this: the Cambrian transition shows when hard body parts evolved. Ancient history is told in terms of pots because baked clay survives better than baskets. That doesn't make pots more important or more numerous than baskets. Palaeontology is constricted into a jigsaw-puzzle of bones, teeth, and shells because those are the bits that are left lying around abundantly and indestructibly. It has got very little to do with what evolved when, or how, or how long it took, or why.
The Isua rocks in Greenland show a carbon-12 ratio indicative of photosynthesis 3.8 thousand million years (3.8 Gyr) ago. The first microfossils, and stromatolite mats built by microorganisms, date from at least 3.5 Gyr ago. Eukaryotes, that is complex internally symbiotic creatures, appear 1.4 Gyr ago and begin to preponderate; their segregated internal chemistry means they can use free oxygen, and the oxygen in the atmosphere increases. This is our kind of life.
Molecular evidence from the DNA of animals suggests they may have existed, as sexual animals, from 1.2 Gyr ago. There is some evidence that eukaryotic algae from the Bitter Springs deposit in central Australia may have been sexually reproducing 900 million years (900 Myr) ago. A more conservative DNA analysis, disallowing some genes, puts the origin of animal life at 700 Myr ago.
Around then, 700 or 670 Myr, was the first great explosion in complex, diverse, multicellular life. The Ediacaran or Vendian fauna has been found all over the world. There was a multiplicity of soft-bodied creatures resembling jellyfish, worms, sponges, and many others. The impressions of their bodies can be beautifully preserved. In many cases these don't look ancestral to modern phyla, however: they appear to be an independent world-wide blossoming of complex life, as the oxygen-rich atmosphere kicked in. It lasted for 100 to 150 million years, only overtaken by the next two diversifications, the Tommotian (in the early Cambrian) and the main Cambrian explosion.
The Tommotian also appears to have been a largely unrelated bloom, not our direct ancestors, but they were the first with recognizable hard parts: palaeobiologists call them "small shelly fauna".
The Cambrian Explosion proper (c. 570-540 Myr) is famous for its radiation of every Bauplan (blueprint, or body-layout) of the modern animal world: arthropods, chordates, annelids, molluscs, and so on. No wholly new animal phylum is known to have evolved since then. It was a tremendously important event in the evolution of life. But four-fifths of the history of life had already happened.
Another explosion has taken place in the last forty years: our understanding of the richness and variation that had already happened before it. No serious scientist believes the Cambrian forms came out of nowhere at the beginning of the Cambrian. What we are seeing is a change in body form that allowed bodies, previous invisible, to become visible.
It affected not only animals, but many other kinds of creatures known from solid fossil evidence to have existed for many hundreds of millons of years beforehand, if not thousands of millions: foraminifera, algae, radiolarians, and so on. This suggests a global change (in the oceans, the only inhabited environment at that time), a shift in the balance of nutrients perhaps. The continuing discovery of our evolution is one of the most beauiful adventures our human intellect is privileged to share.
* Drat, rp beat me to it while I was typing mine.