In The Time of the Doctor, when the Doctor is a old man siting on a chair before he faces the Daleks, Clara says a poem to him:
CLARA: And now it's time for one last bow, like all your other selves. Eleven's hour is over now. The clock is striking twelve's.
What does this poem mean? Does it mean that the end is near like the Doctor’s past regenerations before him — his 11th regeneration is over, now the 12th is coming?
Your interpretation is exactly correct; it's a pretty easy metaphor. Let's go line-by-line:
I'm reminded of Shakespeare, here:
All the world’s a stage,
And all the men and women merely players;
They have their exits and their entrances,
And one man in his time plays many partsAs You Like It Act II Scene VII
A tradition in stage theatre is that, once the performance is ended, the cast comes out on stage and bows to the audience. Since the Doctor's "performance" (i.e. his life) is ending, it's time for him to take his bow (i.e. die).
I'm also reminded of the last words of the composer Beethoven, who also used theatre as a metaphor for life, and the end of a theatrical performance as a metaphor for death:
Friends applaud, the Comedy is over.
This may also be a sly reference to Sherlock Holmes; the story "His Last Bow", published in 1917, is chronologically the last adventure of Sherlock Holmes' life1.
This line is self-explanatory; the Doctor has had many "selves", all of whom have had their "last bow."
In plainest possible English: all of the Doctor's past lives have died, so this one must as well.
This is where the clock metaphor comes in. "Hour" is often used idiomatically to refer to an unspecified period of time; see finest hour. Here, "hour" is being used metaphorically to refer to the span of one's life, so our time is up when our "hour" is up; compare to the classic metaphor of the hourglass2.
"Eleven's hour is over" means that the hour hand is leaving the space of number 11; literally, "Eleven's time is running out."
It's perhaps worth noting at this point that it's fairly common in the fandom to refer to Doctors by their number; One through Twelve3.
With these two facts in mind, the meaning of the line becomes obvious: Doctor number Eleven is dying. In the context of the following line, we might also say that this line is saying "this phase of your life is over."
Recall my thoughts on the clock metaphor in the previous section; having left the space of number eleven, the hour hand is entering the space of number twelve.
When we say a "clock is striking" an hour, we mean that hour has been reached. The idiom comes from striking clocks, which audibly call the hour; Big Ben4 is a famous example.
So Doctor number Twelve is on his way up. In the context of the previous line, a new phase of the Doctor's life is about to begin.
1 Though not the last one published
2 TVTropes link; all hope abandon etc.
3 Personally, I prefer referring to them by actor, but whatever
4 Yes, I know it's not actually called that
In English, "the eleventh hour" means that the clock is reaching the end of the cycle. That is everything is almost over. It is like the "clock striking midnight". Remember that in this story, the Doctor is out of regenerations and Clara has to beg the Time Lords to allow him to regenerate (see other answers on this topic). For example Do the events in Day of The Doctor mean that Peter Capaldi will be the last Doctor?
Although he calls himself the eleventh, the Doctor reveals he's used all of his twelve possible regenerations; his incarnation who fought in the Time War and the Tenth Doctor's aborted regeneration ("Journey's End") are counted. He is therefore in his final, regeneration-less body.
Lying that he won't send Clara back again, the Doctor does so and she returns to Earth as the siege of Trenzalore becomes an all-out war. As the centuries pass, most of the races depart or are destroyed, leaving only the Silence (with whom the Doctor joins forces, putting aside their feud) and the Daleks. On the same day (from Clara's perspective), the TARDIS reappears; Clara enters to find Tasha piloting the TARDIS. Noting "flying the TARDIS was always easy, it's flying the Doctor that I've never quite mastered", Tasha returns her to Trenzalore, as "no one should die alone", sending her to meet the now frail and senile Doctor at the point when the Daleks finally win control of the town. With nothing left, the Doctor goes out to face the Daleks in a final stand. The Eleventh Doctor, about to die from old age, is granted a new regeneration cycle by the Time Lords, subsequently preventing his death and changing his future.
Clara, unable to watch, returns to the crack and, through it, begs the Time Lords to save the Doctor, urging it's owed to him for all he has done in his lives and reminding them that if the Doctor dies, Gallifrey will be lost forever, the crack then closes. The Doctor prepares to die outside, when the crack appears in the night sky. Regeneration energy flows from the crack and into the Doctor, granting him a new regeneration cycle and saving him from death.
The Doctor uses the excess energy of his regeneration to destroy the Daleks. In the aftermath, Clara finds him young again in the TARDIS console room. He explains this rejuvenation is a "reset" for the new regeneration cycle to begin and the changing of his form is taking a while to start up. He delivers a eulogy to his current form, hallucinates a final farewell to Amy Pond, and regenerates. The Twelfth Doctor then declares that the TARDIS is crashing and asks Clara if she knows how to fly it.
