What is it?

The one man who came nearest to reaching God through his own goodness proved to be the chief of sinners.  Ponder Paul's incomparable assets: no soul, before or since, ever held up to the face of God a hand filled with such exquisite pearls.  Circumcised, stamped as God's from infancy; of the stock of Israel, with a blood-right to salvation; of the tribe of Benjamin- a tribe which never  broke away; a Hebrew of Hebrews- a full blooded Jew to the furthest generation back; a Pharisee- intensely orthodox; persecuting the church- on fire for God's law; in the Law blameless- obedient in jot and tittle.  No man ever came so near to winning life through what he was and what he did. "If any other man" (of any age or race or clime) "thinketh to have confidence in the flesh, I yet more"  Paul towers over all legalists for ever. 

But a sudden and awful discovery blasted his prospects. 

"I was alive [in my own eyes] apart from law once: but when the commandment 'thou shalt not lust' came [to his own conscience] sin revived [sprang to life again] and I died [or saw myself a dead man] and the commandment, which was unto life, this I found to be unto death" (Romans 7:9)
"If any man thinketh to have confidence in the flesh, I yet more"

But what had his inward vision revealed?

A corpse before God.  With Paul's failure, the whole world lapses into hopeless despair. 

There next appears a supreme righteousness. 

Whose?   Not Paul's; because he had discovered, with Isaiah, that "we are all as an unclean thing, and all our righteousnesses are as filthy rags" (Isa. 64:6).  He now discovers that what he could not do, Christ did;  that what he could not be, Christ was;  and that Christ had done it, and been it, in order to take his place (2 Cor. 5:21).   He instantly drops his own righteousness, and seizes Christ's.  He exchanges his own pearls for one priceless, flawless gem.  "I do count them but dung, that I may gain Christ, and be found in him not having a righteousness of mine own, but that [righteousness] which is through faith in Christ."
Paul never afterwards doubts his salvation (Romans 8:38): for Christ has kept the Law, not with head, hands, and feet only, but with heart also (Psalms 40:8): and this righteousness is now Paul's (Romans 5:19). The supreme hopelessness is replaced by a supreme salvation. 

There yet remains a supreme uncertainty.  Here are startling words... "Brethren, I count not myself yet to have apprehended but I press on."  (Phil. 3:13)

Not apprehended what?

"If by any means I may attain unto the resurrection from the dead."(Phil. 3:11)

It it most evident that Paul had some special resurrection in view, even the first: and to share in that he was straining every nerve.

But press on to what?

"Towards the goal unto the prize of the high calling."  "IF" [conditional] "by any means" [hazardous] "I may attain unto" [may implying only a possibility i.e., perhaps, maybe] "the  resurrection" [selective] "that which is from among the dead" [exclusive]; it would be difficult to cram a text with more uncertainty that Paul just did! 

As the context suggests, the first resurrection; any reference here to a merely ethical resurrection is wholly out of the question.  That Paul is speaking of bodily resurrection is clear from the closing verse of this very chapter: "we wait for a Saviour who shall fashion a new body of our humiliation, that it may be conformed to the body of his glory."

Every passage that refers to resurrection FROM the dead (Mark 9:10, Luke 10:35, Romans 1:4, Revelation 10:4) refers to physical resurrection. 

Of his resurrection at the end of the world, when all without exception will surely be raised, he could have no possible doubt.  What sense then can this passage have, if it represents him as labouring and suffering merely in order to attain to a resurrection, and as holding this up to view as unattainable unless he should arrive at a high degree of Christian perfection?

On the other hand, let us suppose a first resurrection to be appointed as a special reward of high attainments in Christian virtue, and all seems to be plain and easy.

Paul cannot be speaking of regeneration here because he had already attained that upon his conversion on the plain of Damascus. 

Salvation can never be insecure, but equally true, the Prize can never be assumed until it is won. 

Why?

(1) Because it is a prize.  If the prize be given on faith without works, it is no more a prize.
"Know ye not that they which run in a race all run, but one receiveth the prize? Even so run, that ye may attain"(1 Cor. 9:24).
(2) No splendour of past service can guarantee immunity from backsliding.  None so renounced, so suffered, so served as Paul: yet he assumes no prize!
(3)  False doctrines which rob God of His glory will rob us of ours: therefore "let no man rob you of your prize" (Col. 2:18). 
(4)  Fleshly sins also disqualify.  Therefore "I buffet my body, and bring it into bondage: lest by any means, after that I have preached to others, I myself should be rejected" [for the crown] (1 Cor. 9:24-27).

The insecurity of the chief of apostles binds insecurity of reward for ever on the Church of God. "Not that I have already obtained, or am already made perfect; but I press on, if so be that I may apprehend" :  That is, the apprehension is indissolubly linked with the perfection. 
All therefore culminates in a supreme effort.  "This one thing I do".  Is this for Paul only?

"Let US therefore as many as be perfect, be thus minded".  "SEEK YE FIRST the kingdom of God" (Matthew 6:33) is our Lords words to disciples already in the kingdom mystery.  How?
(1) "Forgetting the things which are behind."   The immeasurable value of the prize may be computed by the immense sacrifices necessary to obtain it.   "The Kingdom of Heaven has no entrance fee, but its subscription is--all that a man hath." Its cost  is a crucified world. 
"Blessed is the man to whom the world, with all her rags of honour, is crucified, and who holds her to be worth no more than a thief on the gallows."  Nothing makes the other world more real, or more blessed, than the renunciation of this.
(2) "Stretching forward to the things that are before."  It is a racer, as Professor Eadie says, in his agony of struggle and hope: every muscle is strained, every vein starting; the chest heaves, and the big drops gather on the brow; the body is bent forward, as if the racer all but touched the goal.  "Let us therefore labour to enter into that Rest, that none [no disciple] fall after the same example of disobedience" (Heb. 4:2) 

Labour?  But I thought salvation was free? I thought it was the gift of grace?   And it is!
But the reward of the Kingdom, the 1000 year Millennial Kingdom of God whereby we gain entrance based upon our righteousness-- the exact kingdom, or prize which Paul has been speaking of is another matter. 

(3) "This one thing I do".  All his missionary ardour, all his thirst for souls, all his toil for the churches, are bent before this overmastering passion of his soul;  because the running tracks for the prize God has laid through these channels of holy service; and today's toil is the measure of tomorrow's glory.  "The first resurrection is a reward for obedience rendered after the acceptance of salvation, and Paul knew not the standard which God had fixed in His own purpose" (G. H. Pember) "The Kingdom of Heaven suffereth violence, and MEN OF VIOLENCE take it by force" (Matthew 11:12) 
(4) It is a calling "upward",  therefore it is God who is calling.  "Walk worthily of God, who is calling you into His own kingdom and glory" (1 Thess. 2:12)  God is calling us from all earthly glories up to the Throne: "that ye may be COUNTED WORTHY of the Kingdom of God, for which also ye suffer" (2 Thess. 1:5)  Did you get that?  Paul is saying that we  suffer to be counted worthy of the Kingdom of God.  He is not saying that we must be be born again. [though that is the first pre-requisite] That is because Paul is not referring to eternal Heaven which we obtain by grace.  He is talking about the coming 1000 year Millennial Kingdom of God.   The cross is ours for ever:  when we have been approved, we receive the Crown (James. 1:12)  We honor God in proportion as we covet His immeasurable rewards.  The apostle not only renounces, he forgets; he not only advances, he presses; he not only gazes, he stretches; he not only does it, but he does it only.  "LET US, THEREFORE, AS MANY AS BE PERFECT, BE THUS MINDED."  "Oh that thought, the hope of the millennial blessedness may animate me to perfect holiness in the fear of God, that I may be accounted worthy to escape the terrible judgments which will make way for that happy state of things, and that I may have part in the first resurrection!" (Fletcher of Madeley).  For "blessed AND HOLY  is he that hath part in the first resurrection: THEY LIVED, AND REIGNED WITH CHRIST A THOUSAND YEARS" (Revelation 10:4,6)