The general purposes for the letter to the Philippians was for Paul to respond with appreciation for the support and the gifts that he received from the Philippian church through the sending of Epaphroditus (1:3-5, 2:25-30, 4:10, 4:14, 4:18). Second, Paul gives news about his circumstances and the ongoing advancement of the gospel in spite of his imprisonment (1:12ff). Third, although the Philippian church was a thriving Christian community, Paul needed to exhort them to pursue unity in the midst of some problems within the community (2:1-11, 2:14, 4:2) and to stand firm in the faith when experiencing trials provoked by those outside the community (3:2ff).
Philippians 4:10-13 fits within the context of the whole letter due to its focus on personal gratitude for the partnership and support. This passage follows Paul’s flow of thought in the previous sections about rejoicing, trusting in God through prayer (4:4-7) and meditating on whatever is true, noble, right, pure, lovely, admirable, excellent, praiseworthy (4:8). He finishes the previous section by stating, “Whatever you have learned or received or heard from me or seen in me─put into practice and the peace of God will be with you” (4:9). After this statement, it seems as if Paul stops and reflects for a few moments, and then he puts his own words into practice by rejoicing in the Lord for the Philippians and meditating on all the blessings he has received from them throughout the years and more recently in his imprisonment. He also touches upon his trust, contentment and strength in the Lord in whatever circumstance, which personalizes his previous statements about experiencing the peace of God (i.e. 4:4,9).
I greatly rejoice in the Lord that now at last you have renewed your concern for me; as to whom indeed you were thinking, but were lacking opportunity. Not that I am speaking according to lack for I have learned to be content whatever the circumstances. I know what it is to be humbled and I know what it is to abound. In everything and in all things I have learned the secret both to be filled and to hunger, both to have plenty and to have lack. I can do all things through the one strengthening me.
v. 10 After encouraging the Philippian church several times throughout the letter to rejoice (2:18, 2:28-29, 3:1, 4:4), Paul adds to his previous statements of personal rejoicing (1:18, 2:17) by stating I greatly rejoice in the Lord. Paul adds the adverb μεγάλως (megalōs) greatly to this rejoicing statement which he does not include in previous personal rejoicing statements. Thus, the addition gives emphasis to the exuberant and profound manner of his rejoicing in the Lord. Paul continues by giving the reason for his greatly rejoicing by writing that now at last you have renewed your concern for me. The greek word translated renewed is ἀναθάλλω (anathallō). This word appears only in 4:10 in the Greek New Testament and may be defined as “grow up again, bloom again” or “cause to grow or bloom again.” Paul solely uses this word picture of the beautiful process of a flower growing or blooming again in order to describe the concern of the Philippians. The Philippians had shown and continued to show their concern for Paul since the beginning of his gospel ministry, and Paul again acknowledges this fact by writing, as to whom indeed you were thinking; however, the Philippians encountered a season where they were lacking opportunity to provide supportive gifts to Paul due to his imprisonment.
v. 11 Paul inserts the disclaimer Not that I am speaking according to lack which is similar to his later statement in 4:17 Not that I seek the gift. Paul may have written these statements in view of the the cultural norm of Greek moralists, Stoic philosophers and Cynics to commend those who were completely independant and were content in any situation. Therefore, Paul continues this idea by writing, I have learned to be content whatever the circumstances. He explains later that his contentment involves much more than a psychological pursuit or a physical discipline.
v.12 Here Paul gives a series of contrasting circumstances in which he knows how to be content, to be humbled and to abound…to be filled and to hunger…to have plenty and to have lack. Paul uses the word μυέω (myeō) which appears only in Phil 4:12 in the Greek New Testament. This verb has some cultural connection to the mystery religions of the Greco-Roman world with the meaning of “initiate (into the mysteries),” but in the more general sense it has the meaning of “learn the secret.” Paul uses this term in the general sense but there is likely an “ironical echo of the mysteries” in greek religion, gnostic philosophy and cultic magic. Paul uses this word to explain that he has learned the “secret of faith,” which he summarizes in the next verse.
v. 13 I can do all things through the one strengthening me. Paul shares the secret of his sufficiency and ability in whatever situation, and it is solely through God. Since the preposition ἐν (en) is followed by the dative τῷ (tō) the one, it may be interpreted as a dative of agency, “used to indicate the personal agent by whom the action of action of the verb is accomplished” and thus translated through . Furthermore, Paul uses the word ἐνδυναμόω (endynamoō) which occurs seven other times in the Greek New Testament and may be defined as “strengthen someone or something, to make someone strong in something.” In Paul’s life and ministry he received a continual strengthening. “This strengthening takes the form of support, and is thus to be construed, not in terms of mana, but in terms of a personal relation between Christ and his servant.”
In this passage, the author meant to teach that Christians should rejoice in the Lord for the partnership and support of other Christians and should show concern for others whenever they get the chance. Furthermore, Christians should learn to be content in whatever circumstance because they can do all things through the one strengthening them.
 Walter Bauer et al. A Greek-English Lexicon of the New Testament and Other Early Christian Literature (Chicago, IL : University of Chicago Press, 1957), 53.  Craig S. Keener, IVP Bible Background Commentary : New Testament (Downers Grove, IL: InterVarsity Press, 1993), 566.  Bauer et al., A Greek, 530.  Gerhard Kittel and Gerald Friedrich, eds. Theological Dictionary of the New Testament. Abridged In One Volume by Geoffrey W. Bromiley (Grand Rapids, MI : Eerdmans, 1985), 619.  Daniel B. Wallace Greek Grammar beyond the Basics : an Exegetical Syntax of the New Testament (Grand Rapids, MI : Zondervan, 1996), 163.  Bauer et al., A Greek, 263.  Kittel and Friedrich, Theological, 191.