Fair warning: this answer does not include any actual knowledge of the history of these symbols’ usage in D&D, nor any statements from D&D authors responsible for choosing them. Instead, I am trying to match these symbols to those found elsewhere. Several of them seemed to remind me of alchemical and astrological symbols as used in Europe since Greek times, which is why I began this answer, but more and more of them don’t seem to quite match those, suggesting that these may have been original creations at some point in Dungeons & Dragons history. So this answer is only partial—some ideas for some of the inspiration, some notes of what the symbols are not, etc. But actually tracking down the D&D history here, I leave to others.
Abjuration
A Google search finds other trident-like symbols, especially as an icon of Neptune/Poseidon. At least one source labels a symbol almost exactly like this one as magnesium, but the usual symbol for magnesium is completely different: ⊛ (a circle with an asterisk in the middle, if your font doesn’t render it correctly).
Also similar to the Greek capital letter psi, Ψ, again with some extra cross bars.
But the most convincing comparison—with thanks to @KumosAgosta for pointing it out—is that the symbol is one of the spokes of the Norse rune Ægishjálmr, or Helm of Awe. The rune was responsible for the dragon Fafnir’s invincibility in the Poetic Edda, so it has strong associations with protections (unlike Neptune, Poseidon, magneium, or psi, so far as I know).
Conjuration
This seems to be a stylized version of the symbol for the classical element Earth: 🜃
Could be a reference to the idea of bringing things “to Earth” perhaps? In classical elemental theory, the Earth element was heavily associated with salt, which was often involved in binding circles and the like.
The stylization also suggests horns, which could be a reference to the fiends that are often summoned with Conjuration. The fact that the line is wavy rather than straight doesn’t seem to matter, or at least I cannot find any other symbol that has a wavy line instead.
Divination
I can’t find any symbol remotely like this. I suspect the curvature may have something to do with dowsing rods, which are bent sticks that are supposed to be able to divine the location of water.
Enchantment
The right side of this symbol seems pretty clearly to be the astrological symbol for the constellation Virgo, ♍, which is also used for the alchemical process of distillation. It could, alternatively, be Scorpio, ♏, with a little more curl—Scorpio is associated with the alchemical process of separation.
The left side is a cross. Along with the circle, the cross is the most common symbol in human civilization; literally every culture ever had one or more. The particulars of this cross—longer bottom piece, shorter top piece, left and right arms equal—really do seem to reference the specific cross symbol used by Christianity to represent the Crucifixion. But that is far from certain.
I cannot find any other source that combines these two symbols in this way. I also... do not quite care to try to speculate on the possible ways in which Virgo and the Crucifixion can combine to refer to Enchantment.
Detexify amusingly associates this symbol with a trademark, ™.
Evocation
An oblong version of one astrological symbol for the planet Earth, ⊕, perhaps, plus rays extending from it. Could also be a sun with a cross (though note that “a sun with a cross” is exactly what that Earth symbol is, since a plain circle is often used for the sun), or an eye with a cross.
My actual preferred speculation here is that this is an eye, with a targeting reticle across it. But I cannot find this particular symbol, either, so speculation is all this is.
And, as noted in the comments, @Quadratic Wizard’s speculation that this is just a stylized fireball seems a lot more convincing than my guesses.
Necromancy
This one is pretty straightforward: the Greek capital omega, Ω. As the final letter of the Greek alphabet, omega has been used to refer to “the end” since antiquity, since at least well before Revelations did it. Necromancy is the magic of messing with “the end,” death, hence omega appearing here.
Illusion
An eye, obviously. Because that is what Illusion is concerned with, what is seen or not seen.
Transmutation
The Greek capital pi, Π, with a little tail, and maybe the left leg has a little blade on it—possibly a scalpel? I can’t find any other source that adds that little tail, or that blade, and I’m not sure what they represent. If it is a scalpel, though, the association with surgery and thus body modification seems obvious.
In modern times, pi, but specifically the lower-case pi, π, represents the ratio of a circle’s circumference to its diameter \$\left(\pi = \frac{C}{d}\right)\$. π is of course immensely important to a lot of mathematics, but I’m not quite sure I see how it associates with Transmutation. Π is also used in mathematics, for repeated multiplication, similar to how capital sigma, Σ, is used for repeated addition (Π is the Greek P, for product, and Σ is the Greek S, for sum), but there’s not any clear relationship between that process and Transmutation.
