It is a heavy shoe, often with nailheads covering the sole - to make it last don't ya know. The word was used to describe an Irish or Scottish accent and was originally meant to be derogatory, especially regarding the Irish.

Brogue, a brogan; a stout, heavy leather shoe, resembling in form the French sabot. Applied generally to the pedal coverings of the Scottish Highlanders and the Irish peasantry. It is also applied to a corrupt dialect, or mode of pronunciation; as, spoken with the Irish brogue.

Entry from Everybody's Cyclopedia, 1912.

Brogue (?), n. [Ir. & Gael. brog shoe, hoof.]

1.

A stout, coarse shoe; a brogan.

⇒ In the Highlands of Scotland, the ancient brogue was made of horsehide or deerskin, untanned or tenned with the hair on, gathered round the ankle with a thong. The name was afterward given to any shoe worn as a part of the Highland costume.

Clouted brogues, patched brogues; also, brogues studded with nails. See under Clout, v. t.

2.

A dialectic pronunciation; esp. the Irish manner of pronouncing English.

Or take, Hibernis, thy still ranker brogue. Lloyd.

© Webster 1913.