Now, because this extra step comes on a huge look-up table, many players report that they never used it. It's an extra step of complexity when you're calculating an attack against a humanoid opponent. Plus, there's the whole business of figuring out which armor class type is represented as opposed to armor class -- an enemy using only a shield is armor class type 9, even if it's a magical shield; the table uses these entries to determine the effectiveness of weapons against certain kinds of armor based on their physical characteristics rather than any magical properties. Thus, an extra step to look up when making attacks, and one that most people ignore.
Obviously, this table exists for a reason, and in theory it's that extra modeling step: A sword is less effective against heavy plate armor than it is against mail, for example. But there's another reason, one that's not explained, but becomes evident with some examination.
Flip back a page to weapon damage. A quick look shows that in 1st edition AD&D, the long sword is the king of one-handed weapons. If you're going to be fighting with a one-handed weapon, you take the long sword if you can use it, since its damage output is tops: 1d8 damage against small and medium targets, 1d12 against larger targets. Sure, some two-handed weapons slice better (the two-handed sword is pretty phenomenal), and there are some weapons that come close -- the battle axe rolls in at 1d8/1d4, the morning star at 2d4/1d6+1, the scimitar at 1d8/1d8. Basically, if you're fighting small- or medium-sized targets, there are a few weapons that are pretty comparable; once you're fighting larger targets, the long sword is it, bar none. So you take the long sword, because it's going to give you the best damage output (not to mention that the majority of magical weapons in 1st edition AD&D are magical long swords).
As a game designer, why would you do that? Why make a game where there's a specific choice that is obviously the "best" choice and leave everything else behind? Partly it's the wargame roots; there's a desire to model weapons based on their perceived effectiveness and desirability, and the sword is hard to argue with just in terms of its utility, balance, and chopping/cutting/thrusting power. But there's another reason: the long sword isn't always king.
Flip back to that armor adjustments page. A look at the long sword shows that it takes a -2 on attacks against an enemy wearing plate and carrying a shield, a -1 against a foe with plate alone (no shield), and gains a +1 against an enemy with a shield and no armor, and a +2 against a foe with no shield and no armor. No other modifiers apply. It's pretty across-the-board.
Take a look at the scimitar by comparison. -3 vs. plate and shield, -2 vs. plate alone or chain and shield, -1 vs. chain alone; not so great. But +1 vs. leather or shield, and +3 vs. unarmored opponents! The scimitar is made for draw cuts with its sharp edge, and that's modeled in how it functions against some kinds of armor. If your enemy's wearing mail or plate, the sharp edge is more likely to slide off ineffectively. Against an unarmored foe or one in very light armor, though, it's more likely to make an effective, deep draw cut. That's reflected in its bonus on its attack roll -- a better chance to score a "telling blow" that causes damage.
So if weapons are categorized there according to how they function against armor, let's look at a weapon that seems really suboptimal -- the military pick. It's doing 1d6+1/2d4 damage in the heavy (footman's) size, which is all right but no long sword. It's also a weapon that typically would only be used by a fighter -- clerics can't use it because it's a piercing weapon, thieves and magic-users don't have the training. Why would a fighter take the footman's military pick over the long sword? Check out those armor adjustments! +2 against plate mail, with or without shield! +1 against chain, with or without shield! -1 against shield, leather, or leather and shield, -2 against unarmored -- but you're probably going to hit those guys anyway; they have a lousy armor class. So you bring the military pick in case you run into a heavily armored foe. The force of the swing powering a narrow beak against the armor just busts right through it.
How about the morning star? 2d4/1d6+1 damage is respectable. No modifier vs. plate and shield, but it has a +1 or +2 bonus against everyone else! This is a weapon that's made to mangle anyone on the battlefield, no matter what kind of armor they have. Wearing chain? You get a nasty bruise and a spike in the gut! Leather and shield? The spikes punch through the shield and the weight breaks your arm. Poor unarmored magic-user? That morning star is gonna replace your skull.
Now the poor battle axe isn't that great unless you're fighting a lot of guys in leather armor. Sucks to be a dwarf, I guess. But they do get to use the hammer, which has a very mediocre damage output of 1d4+1/1d4, but takes no penalties to attack anybody and gets a small +1 bonus against enemies in chain or plate without a shield. A good choice for clerics, too, if you need a thrown weapon -- but for melee, your cleric is going to use the awesome footman's flail, which clocks in at 1d6+1/2d4 and scores +2 against plate with or without shield or unshielded chain, +1 against everyone else except a totally unarmored opponent.
The upshot: For all you folks who skipped weapon vs. armor type adjustments, you accidentally made the long sword the undisputed king of the field. 1st edition AD&D may have some strange complexities, but it seems that they're not without reason. Needless detail, or mad genius?