Here's my take on the arcane/divine distinction, spoilered for length:[sblock]
Flavor-wise, the difference between divine and arcane is that divine magic is done at the whims of some higher being or power, where arcane magic is merely the manipulation of energy. A cleric or paladin has to obey his or her god to retain power, and a druid or ranger has to revere nature, and so forth. Wizards manipulate magic as if it were a science, and sorcerers use their own inherent energies. When bards changed from actually being druids and using druid spells to having the stronger music focus, they changed from divine to arcane and now no longer depend on nature for their power. Warlocks in 3e made a pact in their backstory to gain the
ability to use magic, but once it was granted they could use it however they wanted without being subject to the whims of their patron, hence why they're arcane rather than divine; think of it like buying a million minutes and a terabyte of data for your smartphone ahead of time, instead of relying on a monthly deal that can be altered or canceled at any time. That changed in 4e, but the people who made warlocks directly dependent on their patron while using arcane magic are the same people who made Asmodeus a god, so that was also obviously a mistake on their part.
The same holds for other classes in 3e and 4e. Beguiler, dread necromancer, wu jen, warmage, swordmage, artificer? All gain their power from study and inherent power. Spirit shaman, shugenja, favored soul, seeker, avenger? All have a patron they have to please to retain their powers, whether it's a god, the spirits, nature, or whatever. I didn't particularly like the introduction of the Primal power source in 4e because, entirely aside from the fact that introducing yet another magical source meant making the martial classes even more of a minority, in my view there's no need for a third option: either Primal classes worship nature or the spirits and draw on their power, in which case they're divine, or they draw upon nature as a concept or instinctively without needing to worship it and are Arcane. Adding more power sources opens the door for Shadow, Elements, etc. when having broad groupings is more beneficial--and yes, that means that I think Psionics should just be part of Arcane if they're just going to make it "like magic, but with power points" instead of the actually-different psionics systems in AD&D.
Mechanically, arcane and divine magic are split for the same reason the fighter and rogue are split despite most archetypal heroes being both fighter-y and rogue-y: both types of caster are "magic guys," but each of the classic four approach things in different ways. The lines between them have been blurred quite a bit in 3e and 4e as the designers inflated all of the spell lists, but if you look back at AD&D you can see the splits there:
- The fighter and cleric were both "combat" classes while the thief and magic-user were "noncombat" classes: the fighter is obviously combat centric and the cleric has armor and weapon proficiencies, healing and buffing spells, and other combat-relevant stuff, while thieves were really fragile in combat and magic-users wanted to stay far from the front lines with the AD&D spell disruption rules. It's not a complete split, obviously (the cleric had utility spells, the fighter got secondary skills/NWPs, magic-users had iconic offensive spells, and thieves had backstab), but that's where they're comfortable.
- The fighter and magic-user were both "proactive" classes while the cleric and thief were "reactive" classes: fighters and magic-users had strong motivations to seek out confrontation (fighters wanted the magic arms and armor the monsters were wearing and magic-users wanted scrolls and spellbooks to add to their power), had proactive capabilities (fighters killed things, wizards targeted weak spots), and did well on their own (fighters could go all day with some healing and magic-users had a large toolbox of spells), while thieves and clerics had strong motivations to avoid confrontations (thieves would rather sneak around than fight and clerics could only out-fight the fighter a few times a day), had reactive capabilities (thieves dealt with existing traps and clerics cured existing maladies), and didn't do too well on their own (thieves kinda got squished if they couldn't kill something in the first round and clerics were better force-multipliers than solo adventurers).
And, obviously, fighters and thieves had no magic while magic-users and clerics had plenty. Those differences between the classes are what set up the iconic four roles: in combat, you had fighters and clerics on the front lines while the wizard and thief stayed in back or on the sides, and out of combat the thief scouted around and the cleric patched people up while the fighter kept an eye out for monsters and the wizard got the party past obstacles.
Nowadays, of course, the cleric has lots of good blasting and debuffing spells, the thief (now the rogue) is a "striker" who's perfectly comfortable in combat, the wizard is much more resilient and can pump up his combat spells to incredible heights, and the fighter...well, he isn't amazing out of combat, but he has
some noncombat mechanics. Does that mean we should get rid of the distinction between the two mechanically? I don't think so, and in fact I'd rather see classes go
back to having more defined magical niches instead of giving all classes a bit of everything but with slightly different spins.
Even if 5e only preserves the distinction in a few shared features and otherwise blurs the lines a lot, the classes have fairly defined powersets traditionally; even if you didn't
call them divine and arcane it's part of their identity that the cleric heals, the druid does weather stuff, etc. and the arcane classes do different things. Even the areas where they overlap (necromancy, summoning, and blasting, generally) they do things differently: arcane necromancy is more about debuffs, arcane summoning is more about a few big summons, and arcane blasting is highly versatile, while divine necromancy is better at animation, divine summoning is better at lots of minions, and divine blasting favors typeless damage and avoids friendly-fire.
If you were to entirely divorce classes such that they shared no effects in common, that would make it less necessary to have a divine group and an arcane group, but I can't imagine that the designers are going to make
one healing class,
one summoning class, etc., and as long as there's some overlap the theming from shared power sources helps, I think. It actually helps newbies, since you don't have to learn separate rules for the two types of magic but similar effects, playstyles, etc. carry over between classes, making branching out from your first character or narrowing down your choice of initial character easier, and as mentioned it's familiar to returning players and gives them a frame of reference.[/sblock]
TL;DR: Arcane vs. divine isn't a big deal in 3e or more so 4e but it used to matter, it's good that they're drawing on AD&D (where it did matter) for designing the 5e classes, and I think the benefits of keeping the distinction outweigh the questionably benefits of removing it.