"Face-to-face communication" means talking to someone directly, instead of through e-mail, text messages, telephone calls, passing messages to friends, or other indirect ways of communicating.
"Face-to-face" carries a positive meaning. Most people believe it is the best way to communicate with other people. You can use this part of the phrase in other ways, like:
It's so great to finally meet you face-to-face!
I've spoken with him face-to-face a few times, but mostly we communicate through instant messages or texting.
"Face-to-face" is similar to "in person". The differences between them are very small and probably not that important, but the phrase "in person communication" sounds a little strange. An example in which you can use "in person" but not "face-to-face" is:
I'll wait and give it to him in person.