Elements are common patterns of magic that many spirit bearers' power seems to line up into. They're usually a decent shorthand/assumption when working with unfamiliar spirit bearers for what sort of things they might be capable of, or what their style would be.
The commonly recognized elements are:
Water; Flexible, defensive, momentum, battlefield control. Some good tricks to learn: Unseating footing, attacks from unexpected angles.
Fire; Passionate, aggressive, destructive. Some good tricks to learn: Oxygen consumption, direct heat manipulation, inflict burns.
Air; Highly mobile, evasion, indirect attacks. Some good tricks to learn: Flight, dust and sand attacks, air blade.
Earth; Unyielding and direct, either attack or defense. Some good tricks to learn: Quicksand, pebbleshot, rock armor.
Light; Assisting allies, hindering foes, ranged attacks. Some good tricks to learn: Flashbang, healing others, triggers/alarms/mines.
Dark/Shadow; Deceptive, shaping the battlefield. Some good tricks to learn: Confusing fog, energy drain, choking smoke.
The next two are generally recognized but much less common.
Lightning; Fast and destructive, mobile, supporting. Some good tricks to learn: Static-charged skin, PRACTICE CONTROL A LOT
Metal; Defensive, cutting, traps and holding a position. Some good tricks to learn: Barbed wire, caltrops, barriers in general.
Some less-common "elements" with at least a few examples: Plants in general, flowers specifically, ice, steam, salt, sand, poison, jade, solar, lunar, wax, blood, thread, porcelain, pumpkins specifically, glass.
(It goes into a fair bit more detail on all of the above, of course. There's a whole chapter.)