Paul segues[1] from thanking the Father (1:11b-14) to exalting the Son (1:15-20). This is the One we are to honor and serve as Lord (1:10) and King (1:13). Thus, Paul develops for us a high view of Christ as supreme over all things so that we would worship and serve Him for the exalted Son of God that He is.
Image (15a): Paul first identifies Christ in His incarnation[2] as "the image of the invisible God." The incarnate Son is the representation[3] of the invisible God[4] in visible humanity. In His earthly existence, Jesus revealed the Father through His attributes (John 1:14), miracles (John 2:11; 11:40) and words (John 14:10, 24; 17:8).[5] Thus, the Son explained the Father (John 1:18), and He even boldly asserted: "He who has seen Me has seen the Father" (John 14:9).
Firstborn (15b-16): Moreover, He's "the firstborn of all creation." In terms of chronology, the incarnation isn't the first. Christ entered the world long after creation. In terms of status,[6] however, He is the "firstborn," pre-eminent over all things. This exalted status is explained in 1:16, "For by Him all things were created." He is supreme over all because He created them all. All things "in the heavens and on earth, visible and invisible" (even angels![7]) have been created through Him, and for His sake! This is His world, and He is supreme over all!
[1] 1:15 continues the sentence with a relative pronoun ("who [hos (ὅς)]"), not with "He" (NASB).
[2] The apposition "the firstborn of all creation" explains "the image" as Christ's human existence in creation.
[3] "Image [eikōn (εἰκών)]" means a representation or an impression of something in another form, an image.
[4] Scripture attests to God's invisibility. Cf. Ex. 33:20; John 1:18; 1 Tim. 1:17; 6:16; Heb. 11:27; 1 John 4:12.
[5] This display of incarnate glory should not be confused with His eternal glory, set aside at His incarnation and restored to Him at His glorification (John 17:5, 24). With this glory He will return (Matt. 16:27; 25:31).
[6] This word can describe status, not birth order, hence, pre-eminent. This fits His post-creation humanity best.
[7] The phrase "thrones or dominions…" explain the invisible things. These are angels (cf. Eph. 6:12).