It is a phrase that means "to talk at cross-purposes". It is used when describing a situation in which people are not on the same wavelength. You feel that the person who you talk to misses the point of the topic.
I'm not in touch with Ken anymore. I think he is nice but when I talk to him I feel that we're not on the same page.
ケンとはもう連絡を取っていない。彼はいい人だけど、話が噛み合わない気がする。
ケンとはもう連絡を取っていない。彼はいい人だけど、話が噛み合わない気がする。
Amy is talking about her relationship with her boyfriend.
- Meg: You don't look well. Is everything okay?
元気ないね。大丈夫？ - Amy: Um, I got into a little fight with Jim. We ended up quarreling because we talked past each other. Hmm, I feel that I can't get through to him sometimes.
んー、ジムと喧嘩しちゃった。話が噛み合わなくて、遣り合っちゃった(or喧嘩しちゃった)。んー、時々話が通じない気がする。 - Meg: I see. Do you think it comes from linguistic and cultural differences?
そうなんだ。言語や文化の違いだと思う？ - Amy: Hmm, I don't want to think like that and it is not only that. Not being on the same wavelength with your significant other is painful.
んー、そういう風に考えたくないし、それだけじゃないと思う。好きな人と話が噛み合わないのは、辛いな。