When you summon elements, Melia keeps them around (see the floating orb beside her after the execution). You can keep up to three summon orbs, each have boosts when kept (Wind: Agility; Flare: Strength; Earth: Phys. Def.; Ice: Ether Def; Bolt: Ether Att.; Water: HP Regen). Party members near Melia will be affected by these stat boosts while the orbs are around. At a certain amount of time, or once the you discharge the summon orbs (which will be cast as an ether attack against target foes), those stat boosts will be removed. So as a main, summon-discharge tactic is one o Melia's best strategies. Discharging orbs are also done in LIFO (last in, first out) order, so summon first the element with the best stat boosts while keeping the others for attacks.
Also, her Talent Art is only increased when you discharge a summon element. When filled, you have access to some of her strong arts (Burst End and Mind Blast), as well as doubling the effect of summon discharge power/damage.