The leader of the Tefillah is referred to as a חַזַּן. The word חַזַּן, although translated as a cantor, actually comes from the word חֲזוֹן which means vision. Is there a source for this?
The last Mishna Berura in סימן נג [regarding "דין הראוי לירד לפני התבה"] (s'if katan פז) addresses your question.
וקורין שליח-צבור חזן, שצריך לראות האיך יקרא, ותרגום "וירא" וחזי
And we call the prayer-leader a חזן, because he has to see how to pray properly, and the [Aramaic] translation of "וירא" (to see) is "וחזי"
This follows a discussion of how the חזן should read the prayers out of a written text, specifically one written for the חזן, which is assumed to be without ulterior motive (e.g. להתפארות, for self glorification) [although he does write that if the סידור is printed, there is no difference between a personal סידור and the chazzan's סידור].
Fred mentioned in the comments (here and here) that the ספר הערוך defines the term חזן to mean the בעל קריאה, the reader of the Torah, because he needs to see and read the Torah during קריאת התורה. He also relates this to a Gemara in Bava Metzia (93b) that references "חזני מתא" as city watchmen -- the purpose of these "חזנים" (the שליח ציבור and the בעל קריאה) is to [in Fred's words] "oversee the services;" or, as it is used in Shabbos (11a), as the בעל קריאה who [in the words of Rashi there, s.v. החזן] needs to see (רואה or חזי) which סדרא (Torah portion) the little children are studying from Friday night, so that he can prepare the correct reading for the next day.
As a side note, Fred and I disagreed [see comments below] as to whether the Mishna Berura I quoted above deals with the ש"ץ specifically, or if he just takes the idea from the בעל קריאה and applies it to the ש"ץ; Fred adduced proof from the wording of the Mishna Berura, which sounds like the wording of the Mishna in Shabbos. I think MB just takes this idea from the "רד"א" (as the parentheses following his comment attest) ....this disagreement may be settled if the רד"א is shown to come up with this idea himself, or if he takes it from that Mishna in Shabbos....unfortunately, I do not know who the רד"א was or what ספר his תורה may be found in....if anyone knows, please leave a comment below!