Turning and turning in the widening gyre The falcon cannot hear the falconer;
The falcon is described as "turning" in a "widening gyre" until it can no longer "hear the falconer," its human master.
A gyre is a spiral that expands outward as it goes up. Yeats uses the image of gyres frequently in his poems to describe the motion of history toward chaos and instability.
In actual falconry, the bird is not supposed to keep flying in circles forever; it is eventually supposed to come back and land on the falconer’s glove. (Interesting fact: falconers wear heavy gloves to keep the birds from scratching them with their claws.)
Things fall apart; the centre cannot hold;
The "notion" that "things fall apart" could still apply to the falcon, but it’s also vague enough to serve as a transition to the images of more general chaos that follow.
The second part of the line, a declaration that "the centre cannot hold," is full of political implications (like the collapse of centralized order into radicalism). This is the most famous line of the poem: the poem’s "thesis," in a nutshell.
Mere anarchy is loosed upon the world, The blood-dimmed tide is loosed, and everywhere The ceremony of innocence is drowned;
These three lines describe a situation of violence and terror through phrases like "anarchy," "blood-dimmed tide," and "innocence [. . .] drowned." (By the way, "mere" doesn’t mean "only" in this context; it means "total" or "pure.")
Overall, pretty scary stuff.
Also, with words like "tide," "loosed," and "drowned," the poem gives the sensation of water rushing around us. It’s like Noah’s flood all over again, except there’s no orderly line of animals headed two-by-two into a boat.
What’s Yeats referring to here? Is this a future prophecy, the poet’s dream, or maybe a metaphor for Europe at war? There’s really no way to be sure – Yeats doesn’t seem to want us to know too much.
The best lack all conviction, while the worst Are full of passionate intensity.
Who are "the best" and "the worst"?
One way of deciphering them is that Yeats is talking about "the good" and "the bad." But he doesn’t use those words in the poem, and these lines are a clue as to why not.
For one thing, if "the best lack all conviction," can they really be that good? Believing in something enough to act on it is kind of what being good is all about.
On the other hand, "the worst" have all the "intensity" on their side, which is good for them, but definitely not for everyone else.
Think about that time you dropped your lunch in the cafeteria and all the people you hate laughed really hard, and all your friends were too embarrassed to do anything about it. According to Yeats, Europe after the war is kind of like that. Things are so messed up that you can’t tell the good and the bad apart.