Ah the Eclipse Bar. Introduced in Cataclysm to make a visual representation of a set of buffs gained in earlier expansions, the Eclipse Bar saw its nadir in Warlords, when the druid had essentially no impact on its movement. Hey, do you hate the Eclipse Bar? Well, I've got good news for you:
Eclipse Bar Gone!:
Yes, we're talking about Balance Druids. And while there's still a very clear sun/moon theme to your abilities, the Eclipse Bar as a mechanic is gone. Rejoice!
Much like DPS Shamans and Shadow Priests, Balance Druids are getting a new primary resource. They'll still have mana, but it will be represented as a smaller bar below the main one (similar to how it is when they're in Bear or Cat form.) The main bar is Astral Power.
Astral Power is represented by a kind of lavender bar (lighter than Insanity for Shadow) that goes up to 100. Casting certain spells will build it up while others will spend it.
Sun, Moon, and Stars:
Balance still has a kind of celestial theme. You have two main DoTs to maintain, as well as two filler nukes, all four of which generate Astral Power.
Solar Wrath is basically your old Wrath, but really emphasizing the solar nature of it. This is a quick spell that does nature damage to the target and generates 6 Astral Power - it's likely to be your major single-target nuke.
Lunar Strike has a longer cast time and does a bunch of Arcane damage to the target, then splashes nearby enemies for a smaller amount. This generates 10 Astral Power, and is probably going to be your main cleave filler.
However, while Solar Wrath and Lunar Strike play different roles regarding number of enemies, you'll be using both pretty frequently thanks to Starsurge. Starsurge costs 40 Astral Power, is instant, and does a good chunk of Astral damage to the target (I assume this is a mix of Arcane and Nature - they're really playing fast and loose with magic damage types this time around.) In addition, this will give you Lunar and Solar Empowerments, which increase the damage of your next Lunar Strike and your next Solar Wrath, increasing more with Mastery. You can accumulate 3 of each Empowerment (each Solar Wrath or Lunar Strike will only consume and be affected by one stack of the Empowerments.)
Sunfire is one of your two DoTs, dealing a bit of Nature damage to the target and then putting a more substantial DoT for 18 seconds on the target and any other enemy within 5 yards. This generates 3 Astral Power on cast.
Moonfire is similar, hitting for the same initial amount of damage, only as Arcane, and then putting a 22-second DoT on the target (but not affecting anything else.) This can be used in Bear form, which is cool but not terribly relevant for a Balance Druid. It also generates 3 Astral Power on cast.
Starfall is your big AoE spell. It costs 60 Astral Power and you cast it on an area where it deals Astral damage over 8 seconds. It also debuffs each target with Stellar Empowerment, increasing the damage they take from Sunfire and Moonfire, again affected by Mastery.
The Starlight's Gleaming:
In terms of single-target rotation, I think that you'll basically maintain your DoTs and then generally hit Starsurge whenever you have the AP and then consume your Empowerment buffs. If you don't have any Empowerments and you don't have enough Astral Power to cast Starsurge, you'll probably want to use Solar Wrath on single target situations and Lunar Strike against groups.
For larger AoE situations, you'll want to multi-DoT (Sunfire will automatically apply to several targets, which makes this easier) and then cast Starfall when you have the AP. You might need to toss a Lunar Strike or two in there to generate AP to get Starfall up again after it has expired, but you'll focus a bit more on the DoTs.
Your big damage cooldown is Celestial Alignment, which has a 3-minute cooldown. It increases your damage by 30% and the Astral Power generation of Solar Wrath and Lunar Strike by 50% for 15 seconds.
Balance Druids also retain Innervate, which also has a 3-minute cooldown and allows a healer to cast spells without spending any mana for 10 seconds. Certainly good for any time in a fight when there's a lot of raid damage, and that healer will love you for it.