Files cannot be saved in .mesh format.
A mesh must be exported from Blender, which requires a few things,
Blender, Python, Scripts, OgreCommandLineTools, Exporter.
Even then, the process seems to confuse many people. There /is/ a tutorial on it, by Hammy. Granted it's about "how to mesh" I guess, but it's still the same process, converting is basically meshing.
Let's say you have a .obj file.
You'd import it into blender, and then if you had everything you needed downloaded, you'd export it as a mesh.XML, but then you'd have to run OgreXMLConverter on it to even end up with a .mesh file.