What are we to forget, and what are do we to remember? Paul speaks to the Philippians and us.
From my translation and annotated notes on Philippians 3:13-14.
13 Brothers, I do not consider myself to have taken hold of it, but this one thing [I do], forgetting those things which are behind [me] and reaching out for those things which are before [me].
[Paul remembered his past (Philippians 3:4-6, Acts 22:3), his enemies (1 Corinthians 15:32), those who apostatized (2 Timothy 4:10), etc. What does Paul mean by forgetting those things which are behind me? Probably in the sense of goals. The goal he had as a Rabbi and godly Jew was gone. The goal he has now is in verse 14. Let us also forget those goals and have only one goal stated in verse 14].
14 I press on toward the goal of the prize of the upward calling of God in Christ Jesus.
[The Greek word for “goal” is σκοπός skopós (G4649). It means the finish line at the end of the race. Paul endeavors in everything he does to the high calling of Christ Jesus. This “high” is the Greek word ἄνω ánō (G507) and means up in the sense of up in time or place even raising eyelids (John 11:41). It is also used to indicate countries and regions north of one’s present location. So the “upward” in our text could refer to the Rapture call (1 Thessalonians 4:17), God (His worldview, kingdom, lifestyle as God is up in heaven (John 8:23 and Colossians 3:1-2)), the heavenly Jerusalem (the city of our citizenship (Galatians 4:26 and Philippians 3:20)), etc. This calling is not to be an Apostle, pastor, church worker, etc. It is a calling for every Christian to desire, think, speak, and live according to God’s rules and for His glory. Compare Psalm 40:8, 2 Corinthians 4:18, 2 Corinthians 5:9, and Matthew 6:21].