The first half of this verse summarizes 3:4–6. The second half supplies the purpose for what God did.
made us right in his sight (literally having been justified): See Romans 3:20–28; Galatians 2:16–17.
heirs with the hope of eternal life: The Spirit, as mentioned in Titus 3:5, is often connected to our status as heirs (see Romans 8:15–17; 1 Corinthians 6:9–11; Gal 4:6–7; Ephesians 1:13–14).