Like a lot of metaphysical poetry, "The Flower" is built around a central conceit, a complex extended metaphor that shapes and inspires the speaker's thoughts. Here, the conceit is clear from the title: the speaker imagines himself (and every living person) as a flower in God's garden.
Plenty of other writers have used flowers to symbolize the beauty and fragility of human life. Flowers, after all, live only briefly. They're lovely while they're around, but—in the words of another English poet—no sooner do they blossom than they "fall that very hour." Thinking of himself as a flower, the poem's speaker confronts the fact that life is as short as it's sweet. It doesn't do to get too puffed up with self-importance if one's a flower, the poem suggests; no matter how beautifully one blooms, one will soon "wither."
Similarly, the idea of flowers as a symbol of new life is a familiar one. As he imagines himself miraculously recovering his "greenness" in his old age—the traditional "winter" of life—the speaker suggests that God has revived him the way that spring revives the earth, melting all the frosts of "grief." Here, the flower conceit offers an image of eternal renewal and hope.
But down in the poem's roots, there's a rich and novel idea of what else flowers might mean. If the speaker's life has taught him his life is as brief, fragile, and humble as one flower's among many, it has also taught him how such flowers behave. Flowers, he observes, don't strain toward the sun, "groaning" with effort. Rather, they just grow, guided not by their own efforts, but by the order of nature—and thus, in this speaker's view, by the will of God.
In other words: being a flower doesn't just mean being chastened by the thought that life is short and you're not that special—or made hopeful by the thought that, with the help of a merciful God, joy always returns after sorrow. It means learning to humbly accept God's plan, and discovering in that plan the permanent joy of the "garden" of Paradise.