`Staffordshire` is a county — an administrative area, a bit like a 縣 — in the middle of England, north-west of Birmingham. It is a place name, so it takes a capital letter and no "the".

What makes the name worth knowing for a learner is that it stands for a thing, not just a spot on a map. The northern part of the county, around the towns of Stoke-on-Trent, was for two centuries the centre of the British pottery industry — so much so that the area is simply called "the Potteries". The clay and the coal were both in the ground there. Famous makers like Wedgwood and Spode worked there, and "Staffordshire" on the bottom of a plate, or in a phrase like "a Staffordshire figure" or "Staffordshire pottery", tells you the china came from that tradition. Antique dealers still use the word this way. So when you meet it in a sentence about cups and plates, the writer may be talking less about geography than about a kind of quality and a kind of history.

One small thing about pronouncing it: the ending -shire, at the end of a county name, is said weakly — closer to "-sher" than to the word "shire" on its own.