What does the word 'riding' mean in 'west riding of yorkshire'?

In olden days counties were sometimes divided into thirds for administration purposes - these were officially known as 'thirdings', and this was corrupted by usage in evreyday speech to "riding".

Yorkshire is divided into the East Riding, West Riding and North Riding.

Due to some strange civil service thinking, the county of Tipperary in Ireland was divided in two during the days of the British administration in Ireland and has a North Riding and a South Riding - the word 'riding' having become totally disassociated from its origins, as there was never a third riding in Tipperary.