This Gimli acts as essentially a poor-man's Gandalf's Cart for saving cards you've drawn too early but aren't essential to your strategy (Shield of Boromir before its owner, for example). This should of course not be used for essential cards (Aragorn's Bow, Horn of Boromir), but has the advantage of being able to save large Shadow minions for later (The Balrog being an excellent example, as you have no need to keep him around in Fellowship block with The Bridge of Khazad-Dum being a reliable source of drawing it again).

He has a slight survival advantadge over his counterparts Son of Gloin and Dwarf of the Mountain Race: his Aragorn signet allows Aragorn King in Exile to heal him, which is something to consider given the lack of solid healing cards (in FOTR block they only have Dwarven Heart, Still Draws Breath, Mines of Khazad-Dum and A Royal Welcome in their own culture).

Gimli, Dwarf of Erebor is usually used as a splash companion in other culture's decks for his cycling abilities; in a dedicated Dwarf deck Gimli, Son of Gloin is usually a better choice for his guaranteed skirmish boosting.

From the Current Rulings Document - March 2004:

Erratum:
Damage +1.
Fellowship: If the twilight pool has fewer than 2 twilight tokens, add to place a card from hand beneath your draw deck.