To me, it's absolutely obvious.
The dwarves have runic magic - mostly echantments and traps, but going into the field of summoning (golems), and epic-level destruction (runes are basically carving or drawing stuff - now imagine a rune the size of Texas carved by dwarven picks). The magic they use is that of earth and fire, and they are masters of them, but branching into most others requires immense effort.
Humans are wizards and clerics, devoting their lifetimes to studying the secrets of the universe. Being humans, they practice evocation-type (direct damage) schools the most, though don't disregard illusions and enchantments. They use all elemental magic equally easily, but don't excel at anything.
Elves have druids that tap into the power of nature. Their magic focuses on creating and protecting, which means a lot of summoning and alteration. They excel with summons, and magic is the only way to build their most important constructions. Earth and water are specifically powerful elements in elven magic, while fire and dark powers are completely shunned.
Goblins are shamans that hardly ever practice direct damage. They are able to use their shamanic rituals to create creatures, bestow massive curses, and sometimes enchant items. The goblins exclusively use dark powers and fire due to their demon masters, and can never use light or water magic. The upside to their magic is that shamanic magic can call forth the most massive effects, especially if you consider that the amount of energy released through a ritual is directly proportionate to the strength and number of the shamans, and the duration of the ritual.
In short, when attacking a Ancient Red Dragon:
Dwarves engrave a "violent explosion" rune onto a steak and throw it into the dragon's maw.
Humans cast Freeze, then Fireball.
Elves summon three Green Dragons.
Goblins dance around a totem for a week and the dragon dies from spontaneous massive existence failure.