in its most generic sense converts rotary motion into linear motion or vice versa using solid egg-shaped actuators (lobes)¹.
An engine camshaft...
refers to the shaft which houses a series of cams that actuate the opening/closing of the intake and exhaust valves on a four-stroke engine.
A performance camshaft...
is just a camshaft whose lobe profile is tailored to utilize more of an engine's potential.
Here is a visual comparison²:
The performance improvement can come from two types of change:
altered valve lift
usually a higher lift on the lobe, which increases in length of the valve stroke, which allows for more air to enter through the inlet valves, increasing the power potential of the engine.
altered valve timing - essentially modify when the valves open and close, which has an impact on the effective compression ratio, power output, emissions and other things.
Here is a neat diagram summarizing lots of camshaft-related terminology³:
Performance camshafts don't guarantee performance
For several possible reasons. :
the existing camshaft is well-optimized
something else is limiting the engine's potential
ECU maps are not taking advantage of the hardware change
The key thing to remember here is that engine power isn't totally reliant on a single component in most situations. It's usually all about how the different component play in harmony with one another.
¹ - Wikimedia, ² - bestservis.com, ³ - rbracing-rsr.com