Technology is really important to the success or failure of your civilization. There are over 70 techs in the game, and each provides you with a significant advantage in play. Some techs allow you to construct cool new buildings and wonders, others increase the output from your fields and mines, and others still let you build railroads, or advanced weaponry.
It's critically important that your civ remains competitive in the technology race. If you get behind more than a step or two, you'll find yourself facing the same dilemma as the Aztecs, facing Spanish muskets and cannon with obsidian swords and slings. And as history tells us, the side with the advanced technology always wins those encounters.