Herbert uses these three things to carry the theme of the transitory nature of life that his poem has. Day always ends; and "the dew shall weep thy fall". Roses always fade; "thy root is ever in its grave". Spring always turns to summer, fall and winter; "my music shows ye have your closes". He has chosen three elements of nature; another theme in his poem is nature itself, and how it models the natural process of birth and death. So, through nature-a rose, spring, a day-he is able to express his feeling of how life is a cycle of constant renewal, which includes death. Using nature to do so softens the impact of death a bit-it makes it seem less awful and drastic. However, he asserts in the end that we ourselves can soften the blow of death through having "a sweet and virtuous soul," which will survive after death. It is the only thing that lasts. We need not fear death, just as a rose, the day, and spring do not fear it, if we live a virtuous life.
Those are just some ideas; I provided a link below to a more thorough discussion of themes from the poem. Good luck!