What exactly is meant by cylinder head intake/exhaust port volume?
The amount of air that can pass through the intake or exhaust ports as well as the amount of resistance (back pressure) that is required to get to the particular flow quantity. You are trying to reduce the back pressure (energy) required to get to your desired flow rate.
There are two ways of looking at this.
The volume of air that is capable of passing through the exhaust or intake valve at it's maximum open state from the cam. So, valve in the head.
the volume of air that is capable of passing through the exhaust or intake valve with the valve not in the head.
Personally, I never port a head with the valve out method, in terms of measuring. It's a fake number IMO and doesn't apply.
How can this affect the power curve of the engine?
This is too broad because the variables are so vast.
Ultimately you can effect bottom end power or top end power, it just depends on what you are trying to achieve. Air flowing at high rates through a head and over valves acts differently and various speeds measured in CFM (cubic feet per minute). Cutting away material at particular points in the port will have varying effects on power curve depending on what you remove or don't remove.
Typically, the better the head port volume or CFM flow through ports the better the volumetric efficiency, the better the volumetric efficiency the more potential power the ICE can convert.