It means, basically, that life is short and you will soon die so have fun and enjoy your life while you can.
In this poem, Housman is talking about how it seems like life is really short. The speaker is saying this even though he is only 20 years old (that seems young to me now). The speaker is basically saying "I'm 20 and that means I have only 50 years left to enjoy my life." The speaker says "since that's all I have left, I'm going to go out and look at the beautiful trees." In other words, since my life is going to be over before I know it, I want to make sure I have lived it to the fullest.
This lyric, from The Shropshire Lad, may be Housman’s most famous. It has been memorized by many students, and has been read at many interpretive reading competitions. Some readers have queried the meaning of “white” in line 4, and “snow” in line 12, and the age of the speaker has been questioned. But the season of cherry blossoms should not occasion doubt, and the correct subtraction of twenty from threescore years and ten makes the speaker’s age unequivocal. The poem is in the “carpe diem” tradition, although the movement toward life is vitality and appreciation, not seduction. The poem states the message of "live life to the fullest, for it may be too late to change anything when it is over."