“Not that other modes of communication aren't useful, of course.”
You're having a discussion with a friend about the ways that young people communicate these days. You've said that you think face-to-face communication is the best way to communicate with people. But you don't want your friend to think that you dislike email, text messages, and telephone calls. So you say this to reassure them.
Not that other modes of communication aren't useful, of course.
When you want to clarify something that you just said, you can begin your sentence with "Not that..." For example, if you say that you don't like a certain director's movies, you might want to add that you haven't seen all of his movies:
Not that I've seen all of his movies or anything.
When you say this, listeners will understand that you really meant that you don't like the movies by that director which you have seen.
"Not that..." is useful when you say something that might make other people angry at you, or that they might have misunderstood.
Dude, your girlfriend is absolutely gorgeous. Not that I've been looking at her.
A "mode" of communication is one way of communicating with people. Cell phones, email, face-to-face conversations, and writing are all examples of "modes of communication".
The word "modes" means "ways" but it's only used for a couple of topics. One of those topics is communication. Another one is transportation:
Trains are far more energy-efficient than cars, planes, and other modes of transportation.
The phrase "of course" is useful to show that you're saying something that's obviously true.
It's also useful in situations like the one above, where you think that people might misunderstand something that you said. For example, imagine that you made a general comment about people from a certain country. You might worry that listeners will think you're racist. So you can say: