I'm a beginner to computer graphics and am trying to get a better understanding. My professor has discussed fixed function pipeline and shader based programming. How do these two compare to each other? What's the difference?
The fixed-function pipeline is as the name suggests — the functionality is fixed. So someone wrote a list of different ways you'd be permitted to transform and rasterise geometry, and that's everything available. In broad terms, you can do linear transformations and then rasterise by texturing, interpolate a colour across a face, or by combinations and permutations of those things. But more than that, the fixed pipeline enshrines certain deficiencies.
For example, it was obvious at the time of design that there wasn't going to be enough power to compute lighting per pixel. So lighting is computed at vertices and linearly interpolated across the face.
There were some intermediate extensions related to specific effects — dot3 plus cubemaps for per-pixel lighting from a single source, for example — but the programmable pipeline lets you do whatever you want at each stage, giving you complete flexibility.
In the first place that allowed better lighting, then better general special effects (ripples on reflective water, imperfect glass, etc), and more recently has been used for things like deferred rendering that flip the pipeline on its end.
All support for the fixed-functionality pipeline is implemented by programming the programmable pipeline on hardware of the last decade or so. The programmable pipeline is an advance on its predecessor, afforded by hardware improvements.