The land of the Lotos-eaters is a lush, tropical kind of spot, and we hear a lot about the kinds of plants that grow there. That's partly just a way of setting the mood. At the same time, a lot of these flowers are also symbols for much bigger ideas, like time and eternity. Yup, we get all that pontificating in a bunch of little flowers!
Line 47: Here the falling of a rose petal is used as a metaphor for quiet, gentle music. This music is so quiet and calm that it's like a petal hitting the ground. It sounds like they might need to turn it up a little, actually.
Line 56: The connection between poppies and sleep is ancient. As you might know, the drug opium comes from the juice of the poppy, and it's been used as medicine for thousands of years. One of the things the drug does is make you very sleepy. So the poppy has become a symbol of sleep, and Tennyson picks up on that association in this line.
Lines 81-83: Here the life-cycle of a flower is used as a fancy metaphor for the kind of life the sailors would like to live. They want to be like plants—rooted in one spot, growing, blooming, and then dying with no pain or fuss. It sounds a little boring to us, but hey—different strokes for different drug-addled, hypnotized folks, right?