According to Weber, Calvinism was instrumental in allowing capitalism to arise because it instilled in people the sort of constant desire to work hard that capitalism depends on.
Calvinism is a faith that believes in predestination. People are either saved or damned and there is nothing they can do about it. However, people will want to behave well in their lifetimes even so. They will want to do this because their good actions will tend to show that they are probably saved. Their actions cannot save them, but they can give them hope that they will be saved.
What this means is that Calvinists cannot simply be good some of the time. Instead, they feel that they need to be good all of the time in a systematic way. This sort of attitude is essential for the rise of capitalism. Capitalism requires people to be willing to work hard all the time. They cannot simply work when they feel like it. Weber believed that the Catholic Church allowed people to sin, be forgiven, and sin again. This encouraged them to be less consistent in their work habits as well. This was not compatible with capitalism.
Weber, then, believed that Calvinist attitudes led people to form the habits that were necessary for the success of a capitalist system.