This actually a very simple, sweet poem.
In the first stanza, the speaker is walking in the woods in spring, at around Easter time. He sees a cherry tree in full bloom, looking beautiful. The whole first stanza describes the beauty of the cherry tree with its white blossoms in full flower.
In the second stanza, he tells us he is 20 years old. He assumes a life span of about seventy, so realizes he only has 50 more times to catch the brief moment each year when the cherry trees are in bloom. The entire second stanza is about time. The speaker calculates his life span and how many times he will get to see the beauty of the blossoming cherry tree.
Therefore, he says in the third and final stanza, since fifty more times to see the cherry tree in bloom is not that many, he will take the time to fully enjoy these lovely blossoms. He will be conscious not to miss out on this.
The speaker is telling us that life is short—not that much longer, in the grand scheme of things, than the very brief time the cherry tree blossoms each year. We need, therefore, to seize the moments we have and live life to the fullest, not ignoring the simple moments.
I have to say that I personally love this poem: it is simple, traditional (AABB rhymes), has a quiet, sweet, understated tone, and makes a clear point without the speaker indulging in personal angst and self pity about suffering and mortality.