The Monk

Blackmoor Kung Fu
The Monk character class is introduced in Supplement II: Blackmoor. It makes sense in that supplement which also includes The Temple of the Frog in which numerous monks appear. The Monk PC class also makes sense in terms of  1975 (the year Supplement II is released). Bruce Lee died in 1973 after popularizing the "Kung Fu Fighting" style on TV (as Kato in The Green Hornet) and several exciting martial arts movies including Enter the Dragon and Fists of Fury. The "Kung Fu" TV show (starring David Carradine) aired from 1972 to 1975 and chronicled the adventures of a Shaolin monk wandering the old west armed only with his martial art. Meanwhile, White Box, and the new hobby it initiates, invites players to incorporate into their milieu things that excite them.
White Box includes no specific setting and seems to combine a number of influences in the implied setting with emphasis on sword & sorcery fantasy literature. The use of class titles, as well as arms and armor that have their roots in western medieval history suggests some strong ties to that source. Monks with their martial art skills are not a part of that western medieval tradition nor are they common in sword & sorcery sources. I believe the Monk class in Supplement II is an extension of the popularity of eastern martial arts in the popular culture of the 1970's.
The Monk class as described in Supplement II requires a Wisdom score of not less than 15, a Strength score not less than 12 and a Dexterity score of at least 15. Rolling three six sided dice in order for ability scores will produce very few characters who qualify for Monk. I assume that is the point. Monks are a subclass of Cleric and like Clerics must be human, no hobbits, dwarves or elves as PCs among the religious order. Monks may be of any alignment, but most (75%) are Lawful. Monks follow the same rules as Paladins regarding treasure - in other words they are limited to a maximum of four magical items other than weapons, four weapons and only enough wealth to maintain themselves, their men (if any) and a modest castle. As with Paladins, all excess wealth is to be given to a charitable institution or directly to the poor.
The Monk can use any weapon and has the benefit of doing additional damage points with them equal to one-half their level. They can wear no armor (although their unarmored AC improves as they level) and gain special abilities when fighting without weapons. They receive additional attacks and do additional damage while fighting without weapons and may stun an opponent. Monks gain a number of the special abilities of the Thief class including opening locks, removing traps, listening, climbing, moving silently and hiding in shadows. As the Monk gains level, they acquire the ability to speak with animals, then with plants and to heal themselves.
The abilities of the Monk seem consistent with the Bruce Lee character from the movies and I can imagine the Blackmoor Monk character having adventures somewhat like those of Mr. Lee. Being a fantasy character in a fantastic milieu the Asian trappings could be abandoned and an entirely new rationale given for the existence of such a character class should the referee choose. The aesthetic/mystic nature of the Monk's abilities suggest an exceptional human being, which is consistent with the ability score requirements for becoming a Monk. The class name overlaps with western European church monastics and is somewhat confusing in the context of the fantasy genre, but if we divorce ourselves from this anomaly and focus on the unique quality of the created setting, leaving aside historic reference, we can fit the martial arts monk into the milieu (or don't and leave it out).
Because of this mixing of influences east and west, the Monk is perhaps the most controversial of the original edition character classes. As a fan of the Bruce Lee films, I personally like the Monk as a concept, although I have some issues with the complex nature of its execution in Blackmoor. The 'mystic" side of the monk character is used in some systems to give the Monk some "magical" abilities and I think this makes sense. While playing computer RPGs such as Neverwinter Nights, the Monk is my favorite class for a solo adventurer as they seem to me the best single class to "cover all the bases". Inclusion of the Monk class alters the milieu and I can see why a referee might wish to exclude them. At the same time, the monk can be a lot of fun to play. I do think of the monk as more of a "loner" type, but maybe that is the influence of my associating the class with the characters played by Bruce Lee and David Carradine.