This is one of the rights that were granted to some tenants under the medieval feudal system; it allowed them to take wood from the estates of the manor. It has almost totally died out except as a esoteric historical term, though a very few people still retain the right, for example in the ancient New Forest in southern England (which was indeed once new, but that was shortly after the Norman Conquest, more than 900 years ago).
It’s usually described as the right to take dead wood for fuel. This was certainly one of its meanings (though the supposed rule that you were allowed to take dead branches by hook or by crook, that is, by using only a blunt instrument to pull down dead wood, is almost certainly a folk etymology, as even the earliest recorded examples of that phrase have it in the modern sense of “by any means possible”).
However, estovers was a much broader term than that. It encompassed any legitimate cutting of timber, for a variety of purposes. Before the word came into the language in the thirteenth century, such a right was usually called a boot or a bote, from Old English bot, an expiation, compensation or remedy, literally a making better. (Our fossil phrase to boot, as well as or in addition to, comes from the same source.) In this situation it meant something useful or profitable. Examples were housebote, the right to take timber with which to repair your house; haybote or hedgebote, to repair fences, and ploughbote, to repair agricultural implements. Another was firebote, which was the one that referred specifically to fuel.
Estovers is from Old French estovoir, to be necessary. So they were literally the necessities allowed by law. In later centuries, the term was extended to refer to an allowance of food and clothing to imprisoned felons, and to a pension given to a widow.