The falcon is a proud bird, and it appears often in literature, symbolizing a variety of ideas. Shakespeare uses falcon imagery in Othello, when Othello characterizes his relationship with Desdemona using falconry imagery:
If I do prove her haggard,
Though that her jesses were my dear heartstrings,
I'd whistle her off and let her down the wind
To prey at fortune.
Here Othello uses "haggard" to mean hawk or falcon, and Othello declares that if Desdemona is not faithful or true (too wild), he will whistle her off, as one does a falcon, and let her go free. In this example, the falcon is a proud bird that can be trained to hunt by the falconer. The falconer either controls the falcon or sets it free. Thus, a husband/wife relationship is symbolized by the relationship between the falconer and falcon.
We see a similar analogy used in Taming of the Shrew, when Petruchio uses falconry imagery to discuss his taming of Kate.
Petruchio attempts to tame his falcon (Kate) by depriving her of food until she "stoops" to obey his commands.
In "The Second Coming," Yeats uses the falcon to symbolize the world that has spun out of control--
The falcon cannot hear the falconer.
In this case, the falcon symbolizes mankind while the falconer symbolizes God. Yeats suggests that we have lost our guide, our structure, our conscience.
The common element in each of these examples is the relationship between the falcon and falconer. The falconer symbolizes the one is control, the tamer, the guide. The falcon symbolizes the one who is beautiful and proud, but needing to be domesticated by the falconer.