Consortium is a fancy word for a group you form for an enterprise beyond what any one member could do alone. All the grocery stores in your neighborhood might form a consortium for the promotion of local strawberries.
Consortium comes from the verb consort, which means "to accompany or associate." Consortium used to mean "fellowship, participation, society," but these days you're more likely to hear consortium for an association of different institutions like schools or companies than, say, a consortium of philosophical frog lovers. Still, consortiums usually preserve the ideals of fellowship, with every member institution chipping in to reach a common goal.