Why was the grand old duke of York matching those poor men up and down hills all day?

I assume you mean marching. I imagine it was to build leg strength an endurance. Strong hearts.

It is a satire on some historical event but I've forgotten what.Something to do with an ineffectual commander who squandered the lives of his men.

He was a sergeant major

To level the bumps in the ground

To break their spirit

He wanted to give you a subject to make posts about.

That is what Englishmen do March March March March and scream God Save the Queen

to get them ready for the hellscape that is war

He sounds like a fascist.