The three-age system of classification for human prehistory is primarily used by archaeologists and paleontologists. It gives a way of classifying human prehistory all the way from the creation of the first stone tools to the beginning of reliable written records and the emergence of modern civilization in Europe with the Roman Empire, around 500 BC.
The famous three ages are the Stone Age (from 2.6 million BC to roughly 3500 BC), the Bronze Age (from 3500 BC to 1200 BC or so), and the Iron Age (from 1200 BC to 500 BC - 500 AD, depending on area). In each respective age, its namesake was the primary material used for human industry and toolmaking.
Evidence of human tool use can be found in fertile valleys in East Africa, where humanity originated. This was when the first part of the three-age system, the Stone Age, began. The first tools were crude stone axes, first with only one shaped face, then two. Over time, a plethora of stone tools were developed, but after that, the basic set of tools did not change appreciably for many hundreds of thousands of years.
In the late Stone Age, an explosion of culture and organization occurred among humanity. Agriculture was invented, hunter-gathering progressively abandoned, and cultures in Europe and Asia flourished. From about 100,000 years ago onward, mankind spread across the globe, colonizing all the major continents.
The Bronze Age, part two in our three-age system, began when people in modern-day Turkey figured out how to smelt copper and tin, alloying them into bronze. Bronze is more durable and resistant to chemical breakdown than copper or tin alone. The number of possible tools, artifacts, and weapons increased drastically over the Stone Age. The feedback cycle between tool creation and its economic and social consequences drove human progress forward at an unprecedented rate. Whereas human culture and civilization stayed practically the same for upwards of a million years, it began to change in noticeable ways on the timescales of centuries for the first time.
The Bronze Age culminated in ironworking, which gave way to the final step in the three-age system, the Iron Age, around 1200 BC. As different cultures in different parts of the world adopted the technology at different times, the transition date is not uniform. Iron is extremely durable and easy to come by, making it preferable to bronze. Iron tools enabled the economic expansion of humanity at a fantastic rate, eventually leading into the modern era. Today archeologists carefully pour over ancient tools using modern analysis techniques, putting all of prehistory into perspective with the three-age system.