A closed mesh is where each triangle's edges match up side by side. An open mesh is where this isn't true such as the model being broken up into parts and pieces. To close a mesh, just have it so that the edges of every triangle in your model's mesh meet up and not be "exposed".

Open meshes can sometimes render faster due to fewer vertices and polygons to render, but don't allow for stencil shadows. Why bother creating more vertices and faces for a part of something you never see such as the underside of a terrain or the roof of a building if you can't get high enough to see it? With open meshes, there's also the advantage of having several small, low-poly models placed in one single entity to speed up rendering of such things.