With the reworking of the system here is a small quote explaining how it works, simply because Blizzard can say it better than I can.

" Here’s how the system works: As you spend points in a given talent tree, you’ll receive three different passive bonuses specific to that tree. The first bonus will increase your damage, healing, or survivability, depending on the intended role of the tree. The second bonus will be related to a stat commonly found on gear desirable to you, such as Haste or Crit. The third bonus will be the most interesting, as it will provide an effect completely unique to that tree -- meaning there will be 30 different bonuses of this nature in the game. This third bonus is the one that will benefit from the Mastery rating found on high-level (level 80 to 85) gear."

• Healing – Improves your healing by X%.
• Meditation – Improves your mana regeneration from Spirit in combat. This would likely replace the existing Meditation talent from the Discipline tree, which many Holy priests consider to be a “must-have.” Regeneration will also probably be determined by whether you are in or out of combat, and not the “five-second rule.
• Radiance – Adds a heal-over-time effect to direct heals, such as Flash Heal. Mastery on gear would boost this bonus, and no other talent tree would grant it.

Discipline Priest

For each talent point spent in the Discipline tree, the priest also gets:

• Healing – Improves your healing by X%.
• Meditation – Improves your mana regeneration from Spirit in combat. This would likely replace the existing Meditation talent.
• Absorption – Improves the amount of damage absorbed by spells such as Power Word: Shield and Divine Aegis. Mastery on gear would boost this bonus, and no other talent tree would grant it.

Frost Death Knight

For each talent point spent in the Frost tree, the death knight also gets:

• Damage – Improves your melee and spell damage by X%.
• Haste – Improves your melee Haste by Y%. This might allow us to remove some of the Haste in the Icy Talons line of talents.
• Runic Power – Improves the rate of runic power generated by abilities. While all death knights want runic power, Frost death knights would generally have more runic power than Blood or Unholy death knights (who would receive a different benefit from their respective trees). An Unholy death knight who sub-specs into Frost would still be able to benefit from this bonus, though because they’re investing fewer talent points, they’d benefit to a smaller degree. Mastery on gear would boost this bonus, and no other talent tree would grant it.

Please continue on to here and read the full article as they explain a bit more in detail how the system operates.

Also in case you missed it, as mentioned earlier Blizzard last week released a full explanation on the stat changes heading into Cataclysm, you can view those here.