In the opening line of the sonnet, the speaker addresses the "bright star" of the title, and he says that he wishes he could be as "steadfast" as the star. To be "steadfast" means to be reliable and dutiful. Later in the poem, the speaker repeats that the quality of the star's that he admires is the quality of always being "still steadfast, still unchangeable." The speaker wants to be "steadfast" like the bright star so that he can watch over, constantly and forever, the woman he loves. Just as the star constantly watches over the "moving waters" of the ocean and the "snow upon the mountains," so too the speaker wants to always watch over his "fair love."
The speaker also suggests that a quality of the star which he admires is its beauty. He describes the star as "bright," and he says that it shines with "splendour." The speaker likely sees the star as beautiful in part because it is constant.
The speaker does also highlight a less attractive quality of the star which he does not wish to imitate. He says that the star shines "in lone splendour" and is "sleepless" while it watches over the oceans and the mountains. The words "lone" and "sleepless" suggest that the life of the star is lonely and restless. This is also suggested when the speaker says that the star is like an "Eremite"—an "Eremite" being a hermit or recluse.