A number of spells such as Phantasmal Force, Wall of Fire, Insect Plague, Conjure Elemental, and Control Weather use the notion of "concentration" as part of the spell's duration. There are also several magic items that make use of "concentration," for example the Ring of Animal Control, Helm of Telepathy, Medallion of ESP, and Wand of Illusion. And of course there's the general rule (B47) that using magic items requires "concentration" as well.
However, there's no real definition of what "concentration" means anywhere, it is defined more-or-less "ad-hoc" in every spell or item description. The glossary of the Basic Set does provide a definition as well:
A character putting all his or her attention on an object or action, during which the character may do nothing else, and which, if distracted (attacked) will cause the concentration to be lost.
That's all fine and dandy, but it doesn't jibe with all the other definitions. Here, in the "official" definition, it's enough to be attacked to become distracted. In the Phantasmal Force description, nothing is said about concentration. The Ring of Animal Control and the Helm of Telepathy are in agreement that the user cannot move while concentrating. However, the Medallion of ESP does allow regular movement while concentrating, just not casting spells or fighting. Insect Plague and Wall of Fire require the caster to remain stationary again. Conjure Elemental and the Wand of Illusion allow half movement but neither casting nor fighting. The Wand of Illusion also states that a successful attack that does damage or a failed save (against charm for example) breaks concentration.
The default answer to all complaints about B/X is of course "this is how it is, it's magical, you're wrong to even think there's something wrong here, move on and play the game" but I don't find that very satisfying. I want B/X to be simple enough for me to memorize, and that requires some "regularity" to the rules. So call me dense or something, but I think "concentration" should mean exactly one thing, not five different things.
At least all the various definition of "concentration" agree that it's not possible to concentrate and cast a spell or attack someone at the same time. So we can start from there.
Next movement. The majority of definitions seems to require remaining stationary, but this doesn't scale to all applications. For example, it is essential for the utility of the Phantasmal Force and Conjure Elemental spells that the caster can move with them to some degree. Think illusion of an ogre moving down a dungeon corridor with the party trailing behind at a distance. Think elemental conjured to help excavate the wizard's dungeon complex. However, I think full movement is too much because then there's literally no penalty that must be paid. Half movement seems quite appropriate though. On top of that, it's in line with "Fighting Withdrawal" in regular combat. The only thing it doesn't line up with is casting a spell in the first place: the rules don't allow for any movement. But I think that "maintaining a spell" should be less stressful than "casting a spell" in the first place, so that's alright with me as well.
Which leaves the question of whether an attack is enough to distract or whether the attack has to do damage. Luckily the expert set comes to our rescue because it finally has a rule for interrupting spell casters (X11):
The caster must inform the DM that a spell is being cast and which spell will be cast before the initiative dice are rolled. If the caster loses the initiative and takes damage or fails a saving throw, the spell is interrupted and lost.
I feel in pretty good company accepting this as the rule for concentration as well. If we don't require damage or a failed save, it is way too easy to interrupt spell casters. The same should be true for concentration which (as I said above) I consider "maintaining a spell" and therefore easier. And distracting someone from an easier task should be harder, if anything. So here's my revised definition for what "concentration" means in B/X and I am happy to apply this rule for all situations where concentration is called for.
A creature concentrating on maintaining a magical effect cannot cast another spell or perform an attack. The creature can move at half speed though. If the creature takes damage or fails a saving throw, however, concentration is lost.
Note that with this understanding of "concentration" as "maintenance" the use of the term "concentration" for casting spells or activating magic items in the first place has to cease. Those things do not allow movement in line with the existing rules. I guess a new question that comes up now is whether someone activating a magic item can be interrupted just like a spell caster, but I'll leave that for another post...