It's the spending power. It's in effect the federal government using its control over the public purse at the federal level to assist the provinces, in this case in the field of education. I suppose the intent is to ensure the level of education, in terms of the institutions and the resources for education, are close to the same across the country, notwithstanding the different resources some provinces may have to support those institutions.
On October 18th, 2011. See this statement in context.