Spell Components were originally based on classical ideas about how magic supposedly worked.
You might manipulate a symbolic representation of the target to affect it or to produce an effect, using a picture or doll to represent your target. Thus the early Egyptian practice of carving representations of enemies where they would be constantly walked on on through more modern voodoo dolls. Saltpeter was extracted from bat guano, and used to make gunpowder - ergo, with enough magical skill, you could use a bit of bat guano to create a massive explosion without all the bother of actually making a keg of gunpowder.
Since "the name is the thing", you could call on the power of an entity by using a symbol that represented it. Thus the protective symbols and invocation of divine authority in classical demonology. Similarly, changing how your pronounced the "true name" of a thing could control or transform it. The first edition Dungeon Masters Guide contained some basic magical diagrams, albeit without any details.
Like produces Like. You see traces of this idea today; "I watered the garden, so it rained!". Thus - if you know how to use magic - a tiny "tin can telephone" can be used to send messages.
Power Components. Pearls ("of great price") and fish bring wisdom in some myths. Inhaling the smoke from rare incenses brings an altered state of consciousness in which can be found divine wisdom, while letting it ascend can carry your words to the gods. There are many styles of divination through special tokens; the I Ching and Tarot is still fairly popular.
An elaborate system of Correspondences associats particular magical effects with specific times, stones or gems, scents, plants, and more. You can buy books - such as the Cunningham's Encyclopedias - listing them at great length.
Contagion, supplications to spirits, and more all appeared in the game.
First Edition even included some fairly elaborate discussions of where the magical energy came from and how it was handled. Spellcasters did mysterious things with strange paraphernalia to produce effects that mundane characters did not understand. Thus the more complex spells had long casting times and were easily interrupted. A bucket of water, or being shoved, would ruin the mightiest spell - and they took long enough to cast that many of the enemy would have a chance to try something like that.
Second Edition - in part thanks to the "Satanic!" rumors - discarded most of the references to how the magic was supposed to "work" in favor of purely game mechanical information. Verbal and Somatic components turned into ways to restrain spellcasters a bit and physical components split into flavor text and expensive stuff that kept powerful spells from being used too often.
Third Edition still listed the flavor text components - in part, I suspect, because older edition gamers expected to see them - but removed their mechanical impact with spell component pouches and/or "eschew materials". This also meant that nobody thought of spells as complex things involving a lot of manipulating components either - which paved the way for the introduction of "concentration" and "standard action" spells. No longer would spellcasters have to be carefully protected if they wanted to cast substantial spells.
Similarly, the physics of the spells was simplified into game mechanics. No longer did you need to worry about backblast from setting off a Fireball in a confined place, or bouncing lightning bolts, or similar problems. No longer were there notes that substituting components could have odd effects on spells (although part of that idea later came back as Metamagical Components).
Thus Spell Component Pouches are a lingering nod to the idea that spellcasters studied secret lore, learned lists of magical components and exotic procedures to use them, and spent a lot of time on their studies rather than just deciding to take a level in wizard this time.