You can read an excellent summary of the poem right here at eNotes at the site linked below. Briefly, the poem is both a declaration of love and a lament that that love can't be eternal.
Tithonus is in love with the goddess of the dawn, Aurora. Because of her love for him, the gods grant Tithonus immortality. However, she forgot to ask that he be given eternal youth. So while he will live forever, he will continue to grow older and older. While he was young, Tithonus felt blessed to be immortal, but as he ages, he begins to resent his lover and the gift she got for him. He laments his lost youth and vitality, and he longs for death. Just the sight of the coming dawn used to inflame his desire for his love, but now in his old age he feels no passion for her.
In Greek mythology, Eos (the Greek name for the Roman goddess Aurora) turned Tithonus into a grasshopper.