A more thorough explanation:

A villein regardant is a type of villein, which is a person who is entirely subject to a lord or attached to a manor, but free in relation to all others. Villein regardant specifically refers to a villein who is annexed to the manor of land.

During the time of the Domesday Inquest, which was shortly after the Norman Conquest, about 40% of households were marked as belonging to villeins. They were the most numerous element in the English population. Villein in gross is another type of villein who was annexed to the person of the lord and transferable by deed from one owner to another.

For example, if a lord owned a manor and the villein regardant worked on the land, they would be entirely subject to the lord's authority and could not leave without permission. They were not slaves, but they were not free to leave the manor either. This type of system was common in medieval Europe.