Mesa is a software 3D driver. It uses the CPU instead of your GPU. I've never had an intel igp on Linux, but it should probably be using intel drivers for 3d, not Mesa.
To the grandparent poster: Like any system component, the best way to upgrade Mesa is to upgrade your OS. Sadly, the latest version of Ubuntu is 11.04, which comes with Mesa 7.10.2, and Firefox blacklists every version of Mesa before 7.10.3, so you'll probably have to wait for 11.10 (or just force-enable webgl).