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A more general form of Francisco's answer is that coisotropic submanifolds are those locally defined as the zero set of some Poisson commuting functions, and Lagrangians are those where the number of independent functions is maximal.

Lagrangian submanifolds have a lot of faces though; for example, the graph of a isomorphism from one symplectic manifold $(M_1,\omega_1)$ to another $(M_2,\omega_2)$ is Lagrangian in the symplectic structure $-\omega_1+\omega_2$ if and only if the map is a symplectomorphism. This fact has led many (myself included) to think of Lagrangian submanifolds of the product of two symplectic manifolds as a sort of "generalized map" between them. In this philosophy, a Lagrangian submanifold inside any symplectic manifold would be a "generalized point."

Coisotropic manifolds are also shadows of the representation theory of a deformation quantization; any such representation must have coisotropic limit (this is essentially Gabber's theorem).theorem) [perhaps it's better to say should have coisotropic limit, for some definition of "should"].

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A more general form of Francisco's answer is that coisotropic submanifolds are those locally defined as the zero set of some Poisson commuting functions, and Lagrangians are those where the number of independent functions is maximal.

Lagrangian submanifolds have a lot of faces though; for example, the graph of a isomorphism from one symplectic manifold $(M_1,\omega_1)$ to another $(M_2,\omega_2)$ is Lagrangian in the symplectic structure $-\omega_1+\omega_2$ if and only if the map is a symplectomorphism. This fact has led many (myself included) to think of Lagrangian submanifolds of the product of two symplectic manifolds as a sort of "generalized map" between them. In this philosophy, a Lagrangian submanifold inside any symplectic manifold would be a "generalized point."

Coisotropic manifolds are also shadows of the representation theory of a deformation quantization; any such representation must have coisotropic limit (this is essentially Gabber's theorem).