The Greek adjective hileos means propitious, gracious, or merciful — describing a deity or person favorably disposed. It has two usages in the New Testament: Matthew 16:22, where Peter says 'Hileos soi, kurie' — 'Far be it from you, Lord!' (a strong negation); and Hebrews 8:12, quoting Jeremiah 31:34: 'I will be merciful [hileos] to their iniquities.' The Hebrews usage is purely theological: God's disposition of mercy toward His people's sins.
In Hebrews 8:12, hileos appears in the quotation of the New Covenant promise from Jeremiah 31: 'For I will be merciful toward their iniquities, and I will remember their sins no more.' This is the culmination of all the propitiation language in the New Testament — God is now fully, freely, finally hileos (propitious/merciful) because Christ has made the ultimate atonement. The mercy seat (hilasterion) has been permanently set up. Divine hostility toward the believer's sin is permanently resolved.