This poem is an allusion to the parable of the ten virgins in Matthew 25:1-13 (NRSV):
‘Then the kingdom of heaven will be like this. Ten bridesmaids took their lamps and went to meet the bridegroom. Five of them were foolish, and five were wise. When the foolish took their lamps, they took no oil with them; but the wise took flasks of oil with their lamps. As the bridegroom was delayed, all of them became drowsy and slept. But at midnight there was a shout, “Look! Here is the bridegroom! Come out to meet him.” Then all those bridesmaids got up and trimmed their lamps. The foolish said to the wise, “Give us some of your oil, for our lamps are going out.” But the wise replied, “No! there will not be enough for you and for us; you had better go to the dealers and buy some for yourselves.” And while they went to buy it, the bridegroom came, and those who were ready went with him into the wedding banquet; and the door was shut. Later the other bridesmaids came also, saying, “Lord, lord, open to us.” But he replied, “Truly I tell you, I do not know you.” Keep awake therefore, for you know neither the day nor the hour.
The wise virgins filled their lamps with oil and waited for the bridegroom to appear. The foolish virgins put off filling their lamps and fell asleep. When the bridegroom came, they were not ready to go with him.
I would say that the speaker is the poet himself, telling us to seize life while we can.
The speaker, while it is vague as to "exactly" who it is, is clearly someone older (and wiser), who is in a position to give advice to "virgins", or youth. The poem can of course be interpreted on a literal level, but it is important to consider a broader picture of the intended audience. This poem embraces the theme of "carpe diem" or "sieze the day." The tone is didactic (instructive) and can be read as a recommendation to ALL youth, not just to female virgins. The first two stanzas describe the constant march of time, but the instruction comes in the last stanza, when the audience is given direction to DO something: "...be not coy, but use your time,/And, while ye may, go marry;
The speaker is most likely an older male and he is addressing all young unmarried women. At the time this poem was written, all young unmarried women were indeed, virgins.
He tells them that time is passing quickly and that they should not wait too long be married as the rosebuds in their cheeks will soon fade and no one will want them once they aren't young and pretty anymore.
He says youth is the best time of life when blood and bodies are warmer, but once you spend your youth and the blood is thinner and not as warm, you are not in the prime of life and not sought after.
So, don't be coy and play hard to get too long or you may find that you have waited too long and you are no longer desirable. Marry while you can...don't tarry! Or you will be stuck thinking of the days when you were young and beautiful and regretting the passing of opportunity.