The original phrase was "Little pitchers have big ears" = little children hear (and understand) more than we think they do. This is a play on the original meaning "Little children hear more than you think, but so do idiots and fools (asses)"

A handle to a pticher is an "ear". Both stupid people and pitches have ears. This would mean that anyone can hear something, even a "pitcher", but it may have little value. So don't pay attention to what stupid people tell you that they have heard.