The term is tossed around a lot when referring to Red Mages, but that's mostly cause it's true. A Red Mage is the Jack of all trades in VanaD'iel. They can heal, they can nuke, they can attack, and they can buff/enfeeble.

Out of all these things, a RDM's specialty is enfeebling. No other class in the game can enfeeble as well as a Red Mage can. RDMs can't heal as well as WHMs, can't nuke as well as BLMs, can't attack as well as other melee classes, but enfeebling is their thing. Later on Refresh and Dispel become a huge part of what a RDM is all about.

If you have a RDM in your party and no other healer, then they really should be the main healer. And while acting as main healer, they should not be meleeing. At all. Not even a little bit.

In the early levels a RDM/WHM's main duties should be first enfeebling, backup healing, nuking and then if they have time, meleeing. Later levels dispel and refresh will be the main priority for most RDMs.

I'm sure Ouch! or some other high level RDM can give you a more detailed answer.