The main quality of the star is that it is eternal. We can see this in the poet's use of the word "steadfast" and in his use of the actual word "eternal" to describe the way that the star watches over the world. This quality is very important for the main point of the poem.
The point of the poem, of course, is the idea that the speaker wants his love to be eternal and steadfast. Because he wants his love to be this way, he compares it to the star and he makes the eternal nature of the star (as opposed to its brightness) the major quality of the star that he emphasizes.