The previous thoughts were extremely lucid. I might also suggest that the glorification of self and the efforts of the individual might be a part of the reason why the Renaissance spread so freely and so abundantly around Europe. In a movement where individual achievement and greatness was not only demanded but openly and widely praised, the movement spread itself as individuals developed new approaches to art, thought, philosophy, and approach to life. In this light, the Renaissance almost spread itself for each individual that contributed something new to the dialogue was a part of the movement, and a part of its spread.
I'll just elaborate slightly on the two answers above. This may not fit with the idealistic view of the Renaissance, but one of the most important factors in the spread of the Renaissance was advancement in ship building. Better, faster, safer ships meant more trade, and more trade meant more money.
Art, mathematics, science, etc., until relatively recently, were cultivated by wealthy white men. They were the only ones with education and leisure time, and those are prerequisites for learning.
More trade meant more money, and more money meant more educated men with leisure time. That helped spread Renaissance ideas. It also, by the way, is one of the main causes of the Renaissance.
The term "Renaissance" literally means "rebirth" in French. This term is used to refer to this period because it is seen as a time of the rebirth of learning in Europe.
I would say that there are two major factors responsible for the spread of Renaissance ideas through Europe.
The first factor is trade and travel. It is largely through this mechanism that the ideas were able to move from place to place. In the Middle Ages, there had been more danger associated with trade and so ideas could not spread as well.
The second factor is the invention of the printing press. This allowed ideas to be printed cheaply and distributed.
Renaissance literally means rebirth. In the 1400's there was an uprise of interest in the world and in art. This time period is also considered the beginning of the modern age.
First of all, the Roman Empire used to rule most of Europe hundreds of years earlier. When the Roman Empire fell, Europe fell along with it into the middle ages. The Romans were superior in their technology and when they fell, their modern advances fell too. Europe had hit rock bottom.
A cultural advancement began to take place after the "Black Death" hit Europe. Many people died and this left a lot of jobs available so the standard of living increased. Many families were able to afford things that they previously could not.
In addition, Italians did a lot of trading with people who had a great deal of ancient Greek writings. When the Italians traded with these people a lot of ideas were shared. Suddenly Europe was struck with this passionate interest to learn about the world around them.
There were many different art forms that developed during the renaissance such as sculpture, painting, and building wonderful and beautiful buildings and structures.