Technology is one of the driving forces behind civilization. Technological advances in agriculture and fishing caused cities to grow and thrive. Technological advances in weaponry and masonry allowed cities to drive off jealous barbarians seeking to steal their food and plunder their wealth. And technological advances in medicine and sanitation fought off the other great threat to civilization – disease.
Players acquire technology by accumulating "science," which represent the amount of science a civilization possesses. Every turn a civilization generates an amount of science that can be used for research. Each technology costs a certain amount of science to learn; the more science generated each turn the shorter the amount of time it takes to research each technology. Players can also obtain technology from some Tribal Villages. This is not guaranteed, but it's another good reason to search them out and claim them before anybody else does.
Most technologies have a "Eureka" objective / bonus. This bonus is a sort of Quest (such as "Meet another Civilization" or "Build a Quarry") which when completed, will award a research credit worth 50% of the science previously needed to unlock that tech. Players can get the research credit whether or not they are currently researching the technology in question.