After the heights of the preceding section, it is easy to skim past these "everyday" matters to get on to the next "good stuff" (usually 3:3-21). But that would be to miss too much. Letters between friends have not changed all that much over the centuries. Besides words about the writer's and recipients' respective situations ("my affairs/your affairs"), they very often included information about the movements of intermediaries, which is what Paul is up to now.
The section is in two parts. First (2:19-24), Paul hopes to send Timothy as soon as the outcome of his imprisonment has been resolved, which he expects to go in his favor. Thus he is confident in the Lord that he himself will come soon, but after he has heard back from Timothy (v. 19). Meanwhile, second (vv. 25-30), he has sent the now-recovered Epaphroditus on ahead with this letter. He owes that to them out of friendship--between him and them, and between them and Epaphroditus. It also gives him opportunity to send this letter in advance.
But why send Timothy at all, given Epaphroditus's return and Paul's own hope to come as soon as possible? And why this order of the two paragraphs, since they are chronologically in reverse? And why "commend" to the Philippians two such well-known brothers? Answers to these questions could tell us a lot about the reasons for the letter.
What Paul has written so far does not imply a desperate situation in Philippi. Yet it is serious enough to warrant the sending of both Epaphroditus with this "prearrival" letter and Timothy, who is to find out about "your affairs" and return, before Paul comes himself. Thus even though Timothy will come later chronologically, his paragraph comes first logically, with its repetition of the phrase "your affairs" (see vv. 19, 20; cf. 1:27) and "my affairs" (v. 23; cf. 1:12), plus echoes of "one's own interests" from 2:4.
Commendation of the bearer of a letter was a frequent component of first-century letters. Both the length and the language of these two "commendations" (Timothy is not even bearing a letter) suggest that these men also serve as exemplary paradigms for the two central concerns that emerged in 1:27--2:4. Timothy models serving the gospel by caring for the needs of others; Epaphroditus models the suffering that accompanies serving the gospel.