Okay, I'm guessing that holy focuses on healing spells so what does discipline and shadow specs do?

Shadow is the damage spec, and Disc was used as the PVP spec for a long time, but it is viable for healing in raids as well.

So what's the difference of holy and disc?

Holy is somewhat better for AoE heals and Disc is better for single target heals. I don't think I've done a heroic or a raid with a priest that's holy yet actually.

Holy Priest is definitely more for group heals and has iffy single target healing at best. It's just been something I wanted to avoid since 3.1 released, because it's just kinda like... ehhhh...

Discipline is pretty nice as a support role. Depending. When spec'd, you get a raid wide buff that reduces damage by 3%, Pain Suppression ability that lowers someone's threat and reduces damage taken, in case they pull aggro and need saving. And then Power Infusion, which reduces mana cost by 20% and casting speed by 20% for 15 seconds on any target. Also does have pretty heavy spot heals, especially with Penance. Since Penance has an instant effect, and then that same effect everyone 1 sec for 2 secs. Hits for a good 12k in those 1.88secs with crits. Is yummy. :3 Also, loads of bubble love.

^ you can tell I haven't healed as Holy since the patch came.