The overall message of this poem is "carpe diem" or "seize the day." A brief analysis follows
Gather ye rosebuds while ye may,
Old Time is still a-flying;
And this same flower that smiles today,
To-morrow will be dying.
(Rosebuds are notoriously short lived. Time is always passing. If you want to gather the best things in life, hurry up.)
The glorious lamp of heaven, the Sun,
The higher he's a-getting;
The sooner will his race be run,
And nearer he's to setting.
(If you don't believe me, watch the sun as days seem to disappear as if in a race.)
That age is best, which is the first,
When youth and blood are warmer;
But being spent, the worse, and worst
Time still succeed the former.
(Live while you are young! You have energy to do so (blood being warm) Time, however, will rob you of your youth, so seize the day!)
Then be not coy, but use your time,
And while ye may go marry;
For having lost but once your prime,
You may for ever tarry.
(Don't be afraid to do things (including sex). You'll be married soon, virgins no longer, and your prime will have passed. Youth will never return, so enjoy it while it lasts. Carpe diem!)