Jamieson, Fausset and Brown on Philippians 2:16

16. Holding forth--to them, and so applying it (the common meaning of the Greek; perhaps here including also the other meaning, "holding fast"). The image of light-bearers or luminaries is carried on from Php 2:15. As the heavenly luminaries' light is closely connected with the life of animals, so ye hold forth the light of Christ's "word" (received from me) which is the "life" of the Gentiles (Joh 1:4; 1Jo 1:1, 5-7). Christ is "the Light of the world" (Joh 8:12); believers are only "light-bearers" reflecting His light.

that I may rejoice in--literally, "with a view to (your being) a subject of rejoicing to me against the day of Christ" (Php 4:1; 2Co 1:14; 1Th 2:19).

that I have not run in vain--that it was not in vain that I labored for your spiritual good.