I am obviously not as eloquent as the quoted articles but will try to explain it in 5 sentences.
1. Think of a two-wheeled (side-by-side) wheel barrow.
2. You pick up the handles.
3. You pull the wheelbarrow and the thing will follow you all the time (you being the centre of gravity = nothing more than point at which all forces get together) from here to china and back.
4. You push the wheelbarrow with the wheels in front of you, you now need to make constant corrections to keep the blasted thing going straight.
5 The 3rd wheel is only to stop the thing from falling for or aft depending whether said craft is a nosewheel job (CofG in front of mainwheels) or tailwheel job (CofG behind the mainwheels)
And thats it.
Groundloop is the situation whereby you have not made enough small corrections to stop the centre of gravity overtaking the mainwheels and the craft making itself into a back to front nosewheel job.
Because on takeoff the prop is pulling on the entire affair and helps preventing the above to happening. But beware it is still possible.
HTH
FD