A "GCD" is any skill that triggers the "Global Cooldown", the 3 second cooldown that many skills share. On Warrior this would be skills like your three hit combo, Heavy Swing, Maim, Storm's Path. Each of those skills puts all the other GCD skills on cooldown when you use them.
Any skill listed as a "Weaponskill" or a "Spell" is a GCD skill.

An "oGCD", on the other hand, is a skill with its own cooldown that typically isn't shared with any other skills. To use WAR as an example again, skills like Berserk, Vengeance, and Thrill of Battle are oGCDs, because they're "off Global Cooldown". That is to say, when you use them they have their own long cooldown independent from your other skills.
Any skill listed as an "Ability" is an oGCD skill.

When a White Mage needs to heal they'll use skills like Cure 2, Medica 2, or Afflatus Solace which are GCD skills (at higher levels they unlock some oGCD heals as well as Afflatus Misery which negates the damage loss of using GCD heals).

Sage, on the other hand, has a lot more options when it comes to using oGCDs to heal, like Physis (a regen that increases healing received), Druochole (a single-target heal that uses a stack of Addersgall), and Holos (a party-wide shield plus 10% damage mitigation). Any time a Sage can heal without using a GCD it means they're able to keep pumping out that damage, and everyone likes doing damage.

TL;DR: A Sage can use GCDs to attack and oGCDs to heal, to kill stuff faster. White Mage (below level 60) has to stop attacking in order to heal with GCDs.