Wikipedia tells us that “stover is the leaves and stalks of field crops, such corn (maize), sorghum or soybean that are commonly left in a field after harvesting the grain.” Meriam Webster’s definition only includes dried corn stalks with ears removed. The term is frequently used to refer to straw, hay or odder fodder for cattle. In Shakespeare’s time it was probably dried grass.
In The Tempest (act iv, sc. 1, 62) Iris, messenger of Juno, addresses Ceres, askin her to come and participate in a masque with she and Juno to celebrate the engagement of Ferdinand and Miranda:
Thy turfy mountains, where live nibbling sheep,
And flat meads thatch’d with Stover, them to keep.
The word stover probably comes from the old French noun “estovoir” meaning “obligation” and the related verb “estover” meaning “to be necessary”. The term is frequently used by writers of Shakespeare’s day.