What is the polygon pour and power plane for in a PCB?
A polygon pour is use to make, typically larger than a trace, arbitrary shapes in copper.
A power plane is usually an internal layer, that is &quot;solid&quot; copper. Typically it is used as either the ground return and/or the power rail. Usually there will be two power planes, one for ground return and another for the power rail.
I use the word typically and usually because, it's just metal, so you can do whatever you want with it. Split planes are an example of this. Also, I've used both polygon pours and split planes to route motor return currents separate from the other copper planes on the PCB.
Per the comments:
A large area of copper can be used for several things:

Thermal Heatsinking
Ground plane
Power plane
Shielding
Low inductance path between several components
High current path between components