This phrase musically demonstrates something in each of the first lines of the hymn's verses. The first two lines of the first verse are "Jesus shall reign where'er the sun / Does its successive journeys run." The "wher'er" is sung to three syllables rather than just two, so there's a representation of the breadth. The same feature is in the fourth verse, which begins "Blessings abound wher'er He reigns." There's a similar feature in the third verse, which begins "People and realms of ev'ry tongue." Here, "ev'ry" is sung to three syllables rather than just two, but there's the same representation of an entirety.
The second verse begins with "To Him shall endless prayer be made." In this line, "endless" is sung to three syllables instead of just two, so there's a representation of the long period of time.
In the fifth verse, the line here is "Let ev'ry creature rise and bring," and the "ris[ing]" is represented by the ascent in the first part of the phrase.
I also noticed something about the third musical phrase:
There's a fairly large musical span (the second measure has D notes in two octaves), and in the first verse, the text here is "His kingdom stretch from shore to shore," so there's a large expanse in both the music and the text.
