In these verses, Paul transitions from the language of economics to that of arduous effort. Previously, he compared values: the base value of his prior life as a Jew and a Pharisee and the surpassing value of Christ. Paul's focus now shifts to hard work. Using language like "pressing on" and "reaching forward," he shows us that valuing Christ should practically translate into earnest effort toward Christ-likeness. And he intends this mindset for all believers.
Strenuous Effort: The main verb in the first two sentences (3:12-14) is one and the same: "I press on" (3:12 and 3:14). With this repetition, Paul shows that this is his singular emphatic commitment. This is the "one thing I do." He presses on. He depicts the Christian life not as a leisurely stroll but as a hot pursuit. It's like stretching out your hand to grasp something distant. This is a strenuous effort. The Christian life has no room for complacency.
Unattained Goal: This stretching posture is also reflected in the unattainable nature of this goal. Paul affirms at the beginning of both sentences that this goal is clearly unattained in his life. He says: "Not that I have already obtained" and that he has not "already become perfect" (3:12). It's the same in the second sentence. He has not "laid hold of it yet", and it's still "what lies ahead" (3:13). This is why he pushes ahead and keeps moving forward. He clearly hasn't arrived yet. With this goal in mind, there is nothing to look back at with a sense of smug accomplishment. Paul even intentionally overlooks them.
Christ-likeness: Well, what is this goal? In one word, it is Christ-likeness. We see this in the prior context, where knowing Christ is expanded as having His resurrection power in us; it is our sharing in His sufferings; it is even us being conformed "to His death" (3:10). This is likeness to Christ. This is also the goal in the next passage as well. When the Lord returns, we will be transformed into His likeness! Now, even if this goal isn't attainable in this life (but it will be in glory!), this should never lead us to defeatism. Our regenerated souls are irresistibly drawn to Christ-likeness. So, like a runner who knows he'll reach the finish line if he doesn't give up, we fix our eyes on the goal, and we run.
A Christian Standard: Paul then points out that this is the standard for all Christians. Although he admits this is the mindset of the mature, he expects that all would attain to this understanding by God's revelation. And for those who already have this knowledge, he calls them to strive for Christ-likeness.
 This is the point of 3:15 ("Let us therefore, as many as are perfect, have this attitude"). Cf. also 3:17.
 "One thing" of 3:13 is to "press on." The two gerunds ("forgetting" and "reaching forward") modify this verb.
 "Press on" is di-ō-kō (διώκω), which can also describe persecution. Cf. 3:6, where "persecutor" is this verb.
 "Reaching forward" is ep-ek-tei-no-mai (ἐπεκτείνομαι), which means "to stretch out," often with the hand.
 This is not to be confused with the attainment to the resurrection (3:11). It was a possibility there, but here not at all. The verb is also different: ka-ta-lam-ba-nō (καταλαμβάνω) here vs. kat-an-ta-ō (καταντάω) there.
 This verb te-lei-o-ō (τελειόω) is not the same as the adjective te-lei-os (τέλειος) in 3:15, meaning "mature."
 The verb epi-lan-tha-no-mai (ἐπιλανθάνομαι) means "to willfully forget" as in "overlook" or "neglect." Cf. Heb. 13:2 and 16. Cf. also Luke 12:6-7. Paul does not specify whether this is his past as a believer or not.
 This is Paul's resounding theme in his epistles, especially, in another prison epistle. We are to attain "to a mature man, to the measure of stature which belongs to the fullness of Christ… grow up in all aspects into Him who is the head, even Christ" (Eph. 4:13-15). We are to "walk in love, just as Christ also loved you" (Eph. 5:2).
 This prior mention of Christ-likeness is the unstated object of "Not that I have already obtained it" (3:12).
 Paul leaves "the upward call of God in Christ Jesus" (3:14) undefined. Then he explains it in 3:20-21 ("transform the body of our humble state into conformity with the body of His glory"). This Christ-likeness is also the "call" of God in Rom. 8:28-30 ("called according to His purpose… conformed to the image of His Son").
 The word for "goal" is sko-pos (σκοπός) which comes the Greek verb sko-pe-ō (σκοπέω) which means to look at something. This is a goal like that in an athletic race. This athletic imagery is also seen in his use of the word for "prize." This is the word bra-bei-on (βραβεῖον) which is also used in 1 Cor. 9:24 where he literally refers to a prize in a footrace ("those who run in a race all run, but only one receives the prize [βραβεῖον]?").
 "Have this attitude" is the same language as 2:5 (phro-ne-ō [φρονέω]) which describes one's mindset.
 NASB's "perfect" is better translated as "mature" (ESV and NKJV). Paul clearly counts himself among these.