...is what, exactly?
In the electricity generation business, demand (or load) management is a huge issue; this is the problem of matching the amount of electrical energy generated to the amount of demand that's present at any given moment. Since electrical energy can't be stored for rapid withdrawal, every watt demanded must be supplied instantly by generating capacity somewhere in the grid.
There are several types of "reserve" that is available throughout the day. Some are more expensive, some are less expensive. Some can be brought on-line very quickly (like in a fraction of a second), others take minutes or even hours to become available.
"Spinning reserve" is reserve that's in the form of generators that are already spinning; it's possible for even a big generator to be supplying just a small fraction of its potential output at a given moment, just like when your car is parked with the engine running; the engine is supplying power for the generator to run the car's electric system, computers, perhaps the air conditioning compressor, but these loads represent just a small fraction of what the engine is capable of, like when you're accelerating onto a highway in heavy traffic, for example.
Since the engine is already spinning, just a quick press on the accelerator will bring that capability "on line" as it were.
Electrical generators are just the same, although the particulars are obviously somewhat different.
"Spinning reserve" is that reserve that the utility company has access to immediately; in fact, it's usually tapped automatically; increased electrical load on the generator (often called an "alternator") increases torque seen by the turbine, which slows down a little bit; electronic sensors immediately sense this, and move a valve to admit more steam (or fuel) to the turbine. This happens in a fraction of a second.
I was once lucky enough to get a tour of a running fossil fuel generating plant. I got to see the main steam valve controlling the flow of steam into the turbine driving a 240MW alternator. The valve stem was literally trembling, making tiny motions up and down as it worked to hold the turbine's output RPM constant, while the people of Asheville North Carolina turned lights, air conditioners, and countless other things on and off.