Reduces the threat generated by your Holy and Discipline spells by X% and reduces the chance your spells will be dispelled by X%.
Silent Resolve is a priest talent that lowers threat generation, as well as gives better resistance to dispel mechanics.
% Threat Reduced
% Dispel Protection
This talent serves dual purposes of threat reduction, as well as dispel resistance, making it useful in both PvP and PvE. The threat reduction on this talent does NOT affect Shadow Spells as of patch 2.0.10.
The dispel resistance provided by this spell is useful almost exclusively in PvP, making it harder for your buffs and debuffs to be dispelled.
As of Patch 2.0.10, Silent Resolve no longer reduces threat generated by Shadow spells. There is some discussion as to whether this reduces the threat generated by using Vampiric Embrace or not. Though Blizzard claims that Silent Resolve does not reduce threat from Vampiric Embrace healing, testing from threat meter authors seems to indicate differently. 
As of Patch 2.4, Silent Resolve affects Surge of Light, Power Infusion, Inspiration, Spirit Tap, Blackout, Levitiate, Shackle Undead, Touch of Weakness, Hex of Weakness, and Symbol of Hope.
As of Patch 3.0.2 this talent has only 3 ranks (still has 20% threat reduction) and the dispel protection is increased to 30% max up from 20%.