Ability scores in D&D have always been a focus of some fascination for me. The first thing you do when you create a character in B/X is roll ability scores, and so ability scores are the first window into who this new character is and what kind of adventurer he or she might be. True, they aren't the most important or essential parts of a character in game terms - in fact, D&D as a system runs perfectly well without any ability scores at all - but they inform the concept of each character, as well as granting a few perks and disadvantages that distinguish different characters in play.
B/X uses the old tried-and-true method of rolling 3d6 six times, and applying the results, in order, to Strength, Intelligence, Wisdom, Dexterity, Constitution, and Charisma. I came to understand that they were arranged that way, at least in part, to set Constitution and Charisma, the two scores which were not prime requisites for any class and could be neither raised nor lowered in the optional adjustment phase, apart from the others.
Once scores are rolled and a class chosen, players are allowed to boost the character's prime requisite ability by lowering other scores, at a ratio of one point gained for every two dropped, with the caveat that no score may be lowered below 9. Only a PR could be raised in this way, and the rules as to which other scores could be lowered by which class were probably the fussiest thing about B/X character creation. We tended to ignore those bits and allow characters to lower any of the first four abilities to raise a prime requisite score. Co and Ch were still off limits.
Scores of 9-12 are considered average, and warrant no bonuses or penalties in play. 13-15 earns a +1 bonus, 16-17 a +2, and 18, the highest possible score, a +3. Conversely, a 6-8 takes a -1 penalty, 4-5 a -2, and 3, the lowest, a -3.
The interesting thing about this method of generating ability scores is that it inclined strongly toward producing PCs with at least one above-average score, that is, one that gains a bonus of +1 or more. Any given score is about 26% likely to be a 13 or higher, and thus result in a bonus, and only about 16.5% of all characters will roll no above-average score at all. With the rules for boosting a prime requisite, that percentage drops even further.
On the flip side, most characters will also have at least one ability that's below average, with each roll being 26% likely to produce an 8 or lower, and only a 16.5% chance to escape with no low scores at all.
The chance of any one ability score being in the average range (9-12) is about 48%. The odds of ALL SIX ability scores being average, however, is less than 2%. This means that the vast majority of characters are going to have both strengths and weaknesses that actually have an impact on play, but the + or - 2s and 3s are reserved for the truly exceptional - the top or bottom 4.6%. That's exactly how I like it.
Contrast this with AD&D 1E, in which bonuses often weren't gained until a score of 15 or 16, and penalties until a score of 5 or 6 going the other way. About 86% of ability scores on 3d6 will be in the "dead zone" of 7-15, and a full 40% of characters rolled will have no adjustments from their abilities. Using one of those average-boosting methods like 4d6-drop-lowest gives things a push toward the upper end of the spectrum, but almost guarantees a lack of low scores, which can be just as interesting to play as high scores.
If you like ability scores which are meaningful through the entire spectrum of possible scores, instead of just at the extremes, the B/X rules deliver quite nicely.