Unable to break into a conversation, no pause in a discussion.
Don't you girls ever shut up? I can't get a word in edgewise.
If you can imagine a string of continuous printed text, and a single word attempting to wedge its way into that text. The easiest way to find space for that word would be to turn that word on its edge, to make it very thin, as in the profile of a printed word. If you can't get the word in edgewise, then there must be no break or room in the text or conversation.