I believe it means that the language you know influences the way you think. This is known as "the Sapir-Whorf hypothesis." The word "channel" here means to restrict, or to guide in a certain direction.
For example, if I only know the color words "green" and "blue," I might look at a something that is teal-colored and actually see it and think of it as blue. A day later, if I were to paint a picture of it, I might use blue paint. My vocabulary channeled my thought. It could only flow in one of two narrow channels, "green" and "blue." Since it isn't green, it must be blue.
But if I know words like "aqua" and "teal" and "turquoise" and "cerulean" I might see it, think of it, and remember it as "teal" and paint it using a mix of green and blue paint.
In George Orwell's great novel, "Nineteen Eighty-Four," the protagonist is on a team of people developing a language called Newspeak:
"The purpose of Newspeak was not only to provide a medium of expression for the world-view and mental habits proper to the devotees of Ingsoc, but to make all other modes of thought impossible. It was intended that when Newspeak had been adopted once and for all and Oldspeak forgotten, a heretical thought — that is, a thought diverging from the principles of Ingsoc — should be literally unthinkable, at least so far as thought is dependent on words."
In other words, Newspeak tried to channel everybody's thought into politically orthodox ways of thinking.