Could someone please explain what "Run Spindump" & "Run System Diagnostics" does in 'Activity Monitor' ?

Good question. You don't need to worry about running those. They will run automatically when needed by the system. The information they generate (some) is sent to apple automatically (unless that setting is disabled).

If you want to look at the output of these files, most can be found in the console (Utility/Console). Open the app and look at all the system messages your Mac generates....on the right hand side I would bet you already have a crash log or spindump that was collected without you even knowing it.

It's useless to most users is the short answer. However it does no harm running it to see what it does.

Spin dump shows for each program that is running, at what point in the program it got to then and what programming libraries it's using. This helps developers of an application that crashed or has bugs. They use it to understand the particular environment under which a program was running then, at what stage in the program it got to when it hang or crashed, for example.

When a program crashes it triggers a spin dump to be sent to Apple who, then, forward it to the developers of the offending program, whether in house, or third party developers. It helps improving quality of software.

As it reveals what programs your computer was running, it is helpful to identify programs that run when they shouldn't, viruses or unwanted programs such as "spigot application manager" that I just discovered running now. I It may also give weak hints of what you were doing then. I wonder if third party developers receive the full thing or just the part concerning their application.

Spindumps are process/application specific. System diagnositcs are system wide. They contain information on hardware, memory maps, threads, .....

They gather reports that can be used later for debugging.