There were so many important technological advances in the Renaissance that it is hard to narrow this question down. I would argue that the most important of these advances was the printing press.
The printing press was so important because it made printed materials much cheaper and more widely available than they ever had been before. This allowed more people to become educated and it allowed ideas to spread rapidly. This facilitated such huge social changes as the Protestant Reformation. People across Europe were able to read religious arguments and think about them for themselves. This led to a fundamental change in society.
The printing press is, in my mind, the most important technological advance of the Renaissance.