Hand hewn is a term that is widely misused today to refer to almost anything with a rustic appearance. The real meaning is actually quite limited in application. Hand hewn refers to a timber that has been converted from a log using only axes -- most commonly a felling axe and a broad axe.
Most people who are "hewing" timbers today are using either a power planer to create a textured surface or are adzing sawn timbers -- both of these methods make an "interesting" texture, but are completely inappropriate for historic work, as the tool marks are completely different than what you see on authentically hewn timber. It is important to note that each hewer leaves behind subtle, tell-tale tool marks that allow an observant person to play detective and determine among other things whether the carpenter was left or right handed, which direction along the timber he was moving as he hewed, how high off the ground the log was, the size of the different axes used, whether one person hewed the entire timber or one man went up one side, while another man went down the other, whether two faces were hewed before the log was rolled, or whether one face was hewn and the log rolled each time.
I am sure that is much more information than most people care to know about how a carpenter swung his axe on a particular day a couple hundred years ago. Nevertheless, it is valuable information when it comes to understanding how a particular building was built; especially in terms of documenting existing timbers to better understand the original techniques or when we need to repair, restore, or replace damaged or missing timbers in a way that is consistent with the original means and methods. It is entirely possible when replacing a timber, to study other contemporary pieces from the same building and then hew the replacement the same way the original was done, reproducing the act of conversion as well as the product. Not only do I believe there is cultural value in this knowledge and skill--keeping alive and in some cases rediscovering the subtleties of a traditional building skill that mostly died--it is simply the most accurate process for reproducing a hewn timber. While I understand that such a level of detailed care is not appropriate for many jobs, occasionally it probably is – when accurately replicating parts of the original process is an important part of the clients program. Or when close just doesn't cut it – such as work done on cultural treasures.
Even on the more everyday projects, I still think it is important to recognize authenticity and to value it enough to avoid cheap imitation.