It's taken a long time to reach OpenGL 3.2 compliance -- Mesa 9.0 with OpenGL 3.1 support came last year. The OpenGL 3.2 specification itself has been out since August of 2009, thus taking Mesa four years to implement as it also took quite a while in reaching OpenGL 3.0 and 3.1 compatibility. OpenGL 3.2 introduced geometry shaders, synchronization primitives, a new multi-sample texture type, and various other new extensions were added to the OpenGL Core Profile.
Meanwhile, the latest upstream Khronos Group specification is OpenGL 4.4. The binary AMD and NVIDIA drivers are capable of OpenGL 4.4 but the open-source drivers are not. The open-source Intel Mesa driver is best conditioned as there's dozens of Open-Source Technology Center employees working on the code and advancing Mesa's GL/GLSL support. The open-source Radeon and Nouveau drivers are still limited to OpenGL 3.1 (or 2.1~3.0 for the Radeon Southern Islands driver and similar for the LLVMpipe driver) and bits of various other GL extensions and GLSL functionality. These other drivers will catch-up in due time.
The last bit that it took Mesa and the Intel driver to support OpenGL 3.2 and GL Shading Language 1.50 was GLSL and Geometry Shaders work. The main item left before reaching OpenGL 3.3 compliance is test-cases for verifying the new GL/GLSL features. For OpenGL 4.x support, there's still a lot of work left as shown by the status table. OpenGL 4.3~4.4 support is not likely for Mesa until 2015 at the earliest.
Mesa 10.0 should be a very exciting release since besides the new OpenGL 3.2 compatibility there's also new hardware enablement, hardware support improvements, new Gallium3D functionality, performance improvements, and much more. You can see some recent open-source Mesa benchmarks from our 16-way Linux graphics card comparison.
Confirmation of Mesa OpenGL 3.2 support was made via the Mesa-dev mailing list.
Some related reading that's worthwhile includes the history of Mesa over 20 years and the current state of Mesa as of September at XDC2013.