The stars mentioned in Act III of Our Town connect to the Act I mention of "the Universe; the Mind of God" and are part of the thematic element thus initiated in Act I. One of Wilder's themes is that humanity is part of that which is big and important, specifically the "Universe" and "the Mind of God." The stars symbolize the "Universe" as part of an age old literary conceit and metaphoric association. The stars also symbolize "the Mind of God" as being one of the most splendid parts of the creation that is attributed to the mind of God.
In Act III, Emily has been advised not to return to the living world, but she does anyway. On her return her reaction is that humans are all "blind" and unseeing of the important human essence of each passing busy moment. She asks her mother while revisiting the land of the living to look at her, just look at her.
The dead characters indirectly respond to Emily's remarks by talking about stars. Though the audience doesn't know that the connection is not necessarily clear to the speakers, we can make the connection back to the address on Jane Crofut's envelope and come to the realization that, indeed, for all the smallness of the routine of daily life--the stirring of oatmeal so it doesn't lump or burn, the watching of eggs so they don't overcook, the giving of speeches and donning of dresses--humanity is part of that which is big, significant and important and thus is even more splendid than the splendorous stars.
As the Stage Manger says in the end of Act III, amidst all "the stars doing their old, old crisscross journeys in the sky," Earth is the only know shinning element in the universe that is "straining," striving--that houses humanity which is "straining," striving--"all the time to make something of itself." The final mention of stars by the Stage Manager puts humanity's desire to "make something of itself" in perspective in relation to that which it is a part of.