Ogre is a rendering engine that can use a variety of renderes rather than an OpenGL implementation such as Mesa. Ogre abstracts away from the actual renderer and it's API to provide a more high-level graphics environment.
Opengl is a very low level library. It does just 3d rendering, there's very little else in there. In order to do anything useful, you will need to write a lot of extra code, or use a library which does it for you.
Glut is an opengl helper library which provides window handling and some input, making it easier to write simple apps. The glut homepage says it's only suitable for small to medium opengl apps.
Ogre is a medium level rendering engine with a massive amount of functionality that opengl doesn't have, such as:
- skeleton and morph animation
- multiple texture formats
- 3d model format
- resource system
- logging system
- tons of maths functions
- scene management
- exporters for popular 3d software
- particle systems
- tons more
Ogre sits on top of opengl (or directx or opengles) and provides all the code you would have needed to write yourself.
For example, if you want an animated character on screen, in pure opengl you'd have to write the animation code yourself, while in ogre it's already done for you.
