An online dictionary defines "assarts" as the clearing of forest land and digging out of roots of forest shrubs. A more useful definition expands the term to include, for the purposes of our understanding, the processes by which the royal forests were diminished or changed in function.
We may, for example, consider the creation of enclosures and parks, the harvesting of timber, the pasturage of livestock, the afforestation resulting when the domain of the royal forest was withdrawn from privately owned land, encroachments, or what often resulted from longstanding encroachments, the sale to an adjacent landowner or village of a right to pasturage, a right to enclose, or a right to cut timber or withies.
In medieval Englande, forests, understood as actual forests with trees and shady spaces, as opposed to the legal establishment known as the royal forest- forests, then, I say, were essential and almost central. They provided timber, coppicing, forage, fuel, meat for the poachers and nobles, nuts for the nut bread that villagers ate in lieu of wheaten or oat bread, chemicals for tanning leather- they were at the center of an economy that burned wood, wore leather, built of stone and wood, and often starved in the winter.
The pressure to assart the royal forests, then, was tremendous, the process started early, and by the thirteenth century the royal forests were in full ebb, probably rivaled in extent by the emparking then under way by local landowners and lords, and physically destroyed by the new and different uses of assartification.
Thus, subsequent efforts by English monarchs to reclaim the assarted land- to be the subject of a future post- were, probably predictably, controversial.