How has Quebec influenced the development of Canadian culture?

The most obvious way in which Quebec has influenced Canadian culture is through its contribution to linguistic diversity in Canada. Because Quebec (like New Brunswick) is Francophone, Canada has two national languages, and every student in Canada must learn both languages. This means that Canadians are familiar with both English and French traditions, something that may perhaps underlie Canada's traditions of multiculturalism and pluralism.
In religion, Quebec had the effect of bringing religious diversity to Canada, in that many of the French settlers were Roman Catholic, as opposed to the Scottish and English settlers of anglophone Canada who were predominantly Protestant. Paradoxically, though, Quebec also has been a bastion of secularism as modeled on post-revolutionary France, with a strong commitment to laïcité.
Politically, Quebec has embraced many progressive values and in some ways moved Canada to the left, especially on social issues. It has also contributed to Canadian literary and artistic culture, as well as cuisine.