where is the Black Country in the UK and how does it get its name.?

Ray is right. It is the district around Dudley, Lye and Stourbridge, now part of the urban agglomeration which includes Birmingham and Wolverhampton.

It had natural resources of iron ore, flowing water and coal and was one of the first places in the world to develop extensive iron-smelting and metal-working industries. These early smelters were very inefficient and consumed huge quantities of coal. The resulting outputs of soot, coal dust and iron dust stained all the local environment, leading to the name.

It is the West Midlands (near Birmingham),

I think, but am not sure, that the name comes from the time of the Industrial Revolution when the area was a hive of industrial activity for which the burning of coal was necessary.

So it is an old industrial part of UK. Many thanks