This passage occurs as a New Testament Lesson in the RCL "Pentecost"/"Ordinary"/"Proper" Season, Year A, most recently September 2014.
Summary: Paul begins to describe two paradoxes of the Christian faith: First, our growth comes about through our decline. Second, our heart is in heaven, but our hands are on earth. Paul continues to work these themes throughout his letter to the Philippians. I offer a third one. Paul talks about the importance of the community giving both a unified and public witness of the faith. My paradox: The more unified, the less public the witness; the more public, the less unified.
ζην ("live"; present infinitive; 1:21). Few translations catch the distinction here for Paul between living and dying. They are not in the same tense; dying is in the aorist (which refers to a one tme event). Paul is not talking about existential dying as he might in other letters. He is refering to his physical death that will lead to heaven: 'Living is Christ; death is gain' is probably a more accurate translation. Or perhaps 'Living is Christ; to die is gain.' Excellent textbook example of the subtleties conveyed in tenses...
καρπος εργου ("fruit of work"; 1:22). The NET translates this word here as 'productive work.' This is the most American translation ever! Paul is not driving toward productivity by modern metrics. He is using the biblical idea of bearing fruit in Christ. Keep it as fruit and help the reader see Paul's connections to other places in Scripture (including the Gospel for today).
επιθυμια ("desire"; 1:23) Paul uses the word "desire" here, which he will elsewhere caution Christians against (make no provision for the flesh to gratify its desires...Romans 13:14). There is something intensely emotional about Paul's relationship with Jesus Christ.
προκοπη ("advancement"; 1:25) I assert that Paul's letter to the Philippians picks up this theme: Christian advancement; what does Christian maturity look like? Paul boasts in Galatians that he had progressed in his Judaism (1:14) but then indicates this was not really gain at all. The root of this word is "cut" κοπτω; pioneers were cutting ahead in order to make advancement. For Paul, advancement in Christ -- "sanctification" -- is related to being cut off, to having our plans, our pride and even our habits amended, if not ended.
περισσευη ("overflow" or "excess"; 1:25) This word is not that remarkable in this context, but provides a nice contrast to the believe in scarcity found in this week's Gospel, Matthew 20:1-16
πολιτευεσθε ("live" from πολιτευομαι, 1:27) This verse means not simply to live, but live as a citizen. Paul does not use this word elsewhere; why? I assert this is because Philippi was a Roman colony run by military heros turned citizens. The idea of citizenship would have been important for his hearers. Paul continues this theme, even discussing a heavenly citizenship (3:20). Here Paul begins to contrast citizenship in this world and in Christ's kingdom. Worth noting is that this verb is in the plural! Paul exhorts them all together.
συναθλουντες ("work together" from συναθλεω; 1:27) Paul also commends people "in one spirit to fight/work together." Note: In 4:3 he thanks God for the women who have done precisely this. The root word here "αθλεω," from which comes our word for athelete. Today this has connotations of merely sport, but in ancient Greek it means more broadly means battle or contest. Paul is emphasizing first the challenge of Christian life, but also the importance of a) unified and b) public witness for faith which must be made. As Paul notes, he should be able to hear and see the witness of the church!
πασχειν ("suffer" 1:29) and αγωνα ("struggle" literally agony); reminders of what our sanctification means for us, to return to the idea of being cut off.
Grammar: Simple infinitive
Paul uses simple infnitives throughout this section: το ζην "The living" e.g. το αποθανειν, The dying (21); το επιμενειν, the remaining (24).
An infinitive is simply a verb that has not been conjugated; it is unclear who is doing the action. In English, infinitives take to forms, here with the verb "run": "to run" and "running." These are fairly easy to translate, because they function like English. They allow a verb to behave like a noun: "The remaining here is better." (Perhaps in English a good example is: "I like running")
I call them simple because Greek can use the infinitive in some pretty striking ways, but here Paul is simply using a verb as a noun as a way to emphasize the act but still treat it like a noun.
One example of how Greek can use an infinitive is found in verse 29: το εις αυτον πιστευειν (29)
Here this means "the believing in him"; Paul could have said, "the faith in him" but by using an infinitive it draws attention to the action. In this case, the Greek is doing something that English should not, namely split an infinitive, this time with lots of information!