For your average medieval person living in an area that logistically allowed for it, hunting game (even in the form of poaching) was a way to get by. It was a way to supplement your regular diet, and if you did it right it was free. (If you did it wrong, you were in a lot of trouble.) But for medieval noblemen and women it became an art, a sport, and a status symbol -- perhaps because they didn't necessarily need to hunt those animals down themselves if they wanted to eat meat. Hunting itself was ubiquitous throughout the entire Middle Ages and likely throughout history, but the medieval European hunt as an aristocratic custom and pastime reached its fullest flower in the 14th and 15th centuries; I don't think it's a coincidence that this is also where texts describing how and what to hunt (written both for the delight of genteel audiences and as advice for the staff that would help them) also proliferate.
For a look at literary constructions of medieval hunting, you could do worse than to look at Gaston Phoebus' Livre de chasse -- Gaston III, count of Foix, viscount of Béarn, was an authentic French nobleman of the second half of the 14th century with a nobleman's concerns. The chronicler Froissart describes Gaston in some detail, but among his remarks is this:
He mightily loved dogs above all other animals; and during the summer and winter amused himself much with hunting.
One of those dogs comes to save Gaston's life later when it's used as an unwitting test for poison, administered to Gaston by his own son (Also named Gaston.) In general, the keeping of dogs as nobles' pets owes a lot to the practice of hunting using hounds, even if the later development into dogs that are more recognizably lapdogs defeats that purpose somewhat.
Gaston Phoebus wrote his Livre de chasse some time in the late 1380s, dedicating it to Philip the Bold, and it became one of the most broadly-disseminated texts on aristocratic hunting -- this might account for how many surviving manuscripts of it exist. (The English translation of Phoebus' text, The Master of Game, is also the product of an aristocratic writer -- Edward of Norwich, Duke of York. His edition is dedicated to the future Henry V of England.) It's a four-part treatise covering the benefits of hunting, the best ways to go about it, the qualities of different game and how to hunt them, as well as why men should hunt at all.
Furthermore I will prove by sundry reasons in this little prologue, that the life of no man that useth gentle game and disport be less displeasable unto God than the life of a perfect and skilful hunter, or from which more good cometh. The first reason is that hunting causeth a man to eschew the seven deadly sins. Secondly men are better when riding, more just and more understanding, and more alert and more at ease and more undertaking, and better knowing of all countries and all passages; in short and long all good customs and manners cometh thereof, and the health of man and of his soul. For he that fleeth the seven deadly sins as we believe, he shall be saved, therefore a good hunter shall be saved, and in this world have joy enough and of gladness and of solace, so that he keep himself from two things. One is that he leave not the knowledge nor the service of God, from whom all good cometh, for his hunting. The second that he lose not the service of his master for his hunting, nor his own duties which might profit him most. Now shall I prove how a hunter may not fall into any of the seven deadly sins. When a man is idle and reckless without work, and be not occupied in doing some thing, he abides in his bed or in his chamber, a thing which draweth men to imaginations of fleshly lust and pleasure. For such men have no wish but always to abide in one place, and think in pride, or in avarice, or in wrath, or in sloth, or in gluttony, or in lechery, or in envy. For the imagination of men rather turns to evil than to good, for the three enemies which mankind hath, are the devil, the world and the flesh, and this is proved enough.
These are some pretty lofty aims that expand far beyond putting meat on the table. Phoebus details how to go about hunting harts, boars, wolves, and roe deer, as well as otters, badgers, hares, and foxes, and he deals with what we'd now call broadly "deer" in terms of their different life stages and how that dictated their qualities. From Norwich's translation, regarding the hart:
The hart is a common beast enough and therefore me needeth not to tell of his making, for there be few folk that have not seen some. The harts be the lightest beasts and strongest, and of marvellous great cunning. They are in their love, which men call rut, about the time of the Holy Rood in September and remain in their hot love a whole month and ere they be fully out thereof they abide [in rut] nigh two months. And then they are bold, and run upon men as a wild boar would do if he were hunted. [...] he smiteth as the stroke of the springole, for he has great strength in the head and the body. They slay, fight and hurt each other, when they be in rut, that is to say in their love, and they sing in their language [Norwich adds 'that in England hunters call bellowing'] as man that loveth paramour. They slay hounds and horses and men at that time and turn to the abbay ['be at bay'] as a boar does especially when they be weary.
This isn't a 101-level text; it's clearly for people who know their stuff, or who would like to learn their stuff. He goes on to describe other actions of the hart by the season in which they occur, the behavior of harts when young and old, how harts seek to evade hunters by concealing their smell from the hounds, and so on in quite fine-grained detail for the other animals he describes as well. It's a mix of Gaston's (and Norwich's) folkloric understanding of the animal kingdom (harts live to be a hundred years old) and their practical understanding of it gained from practical experience as well as the study of other hunting texts. Illustrations on both version of the text showcase both the practical and the aesthetic concerns of hunting -- this scene of men on horseback accompanied by men on foot hunting the roebuck shows the trappings of hunting (hounds, horns, swords and spears) as well as the excitement of the pursuit.
It took resources to put together a formal hunting party this way -- it took time and money to maintain horses and dogs as well as to employ lymerers (guys whose whole purpose is to act as handlers for scenthounds) and other staff to smooth the process along, and one had to be of a certain social class to access forests and game reserves, hence all the poaching. A host of weapons were employed (not just the bow and arrow we associate with genteel medieval hunting -- things could get pretty down and dirty) and aristocratic women might well be involved, even if their use of weapons (and birds of prey, in the case of falconry) had a gendered element. The birds one might keep and use for the purpose of hunting were closely dictated in such manuals along the lines of rank and class, not unlike sumptuary restrictions -- in Juliana Berners' 14th-century guide to falconry she dictates that gyrfalcons are for kings, merlins for ladies, goshawks for yeomen, and sparrowhawks for priests. (Berners herself may have been an abbess; well-off clergy weren't above hunting as a pastime.) This was nominally due to practical concerns (how could a gentle lady wrangle a massive bird of prey? how could a poor man afford an expensive bird more fitting to an emperor?) but primarily due to the aesthetics and social cachet of each kind of bird, just as sartorial restrictions on who could wear which velvet or what fur lining on garments served a practical purpose primarily to back up their social purpose.
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