TITLE: What is a Lagrangian submanifold?
QUESTION [6 upvotes]: I see references to Lagrangian Submanifolds in the literature but don't know what they are. Is there a relation to Lagrangian Tori (which I also don't know what are). Could someone give a definition that includes an intuitive explanation for what their use is?

REPLY [2 votes]: It's a special kind of submanifold of a symplectic manifold; see the definition on Wikipedia. There was a question about this on Math Overflow not long ago, where you will find some good answers.