The quote is, of course, from Samuel Taylor Coleridge's Rime of the Ancient Mariner. In the poem, the mariner, an old sailor, stops one of three wedding guests. He is compelled by his experiences to relate his story. He chooses the wedding guest who inquires why he has been stopped?
By thy long grey beard and glittering eye,
Now wherefore stopp'st thou me?
Originally the Mariner stops the guest to compel him to listen by holding him with his hand. This provokes an agitated response from the guest, not only at being stopped but also at being touched:
He holds him with his skinny hand,
"There was a ship," quoth he.
`Hold off! unhand me, grey-beard loon!'
Eftsoons his hand dropped he.
Even so, the mariner manages to holds the guest's attention by looking at him with his glittering eye. The guest is mesmerized by the mariner's gaze, and sits upon a stone to listen. The mariner was compelled to share his story, and now the wedding guest is compelled to listen:
He holds him with his glittering eye -
The Wedding-Guest stood still,
And listens like a three years' child:
The Mariner hath his will.
The Wedding-Guest sat on a stone:
He cannot choose but hear;
And thus spake on that ancient man,
The bright-eyed Mariner.
So, by stating that "the Mariner hath his will," Coleridge means that he has succeeded in compelling this perfect stranger, the wedding guest, to listen to the tale he must tell. It should be remembered, too that the mariner was as compelled to tell the story of his strange adventure as was the wedding guest to hear it:
I pass, like night, from land to land;
I have strange power of speech;
That moment that his face I see,
I know the man that must hear me:
To him my tale I teach.