The cambrian explosion was an evolutionary event that occurred around 541 m.y.a. (read as million years ago) where most of the animal phyla started appearing in fossil records. A phylum is a level of classification in biology that is one level below the kingdom. Almost all present animal phyla appeared during this period. The event lasted for about 20 to 25 million years. A leading theory for the cause of this event is the increase in oxygen levels in the atmosphere. Earth's atmosphere did not contain free oxygen. The oxygen that is currently part of the atmosphere is the result of billions of years of photosynthesis. Metabolic functions may have been slowed down due to the lack of oxygen prior to the cambrian explosion. For example, the creation of thetissue, which is required for hard exoskeletons. This also explain why there are very little fossils prior to this period.
In our times, there are some events that can be considered as an explosion of development. Maybe the technological cambrian explosion could be the invention of electricity or the transistor. One fundamental technological change that then had profound effects on all aspects of life. Probably writing is the cambrian explosion equivalent pre-technology times. That became the primary way in which we stored and transferred knowledge across generations. Leading to an advancement based on past experiences and mistakes.