Simply put, it's how you talk to yourself.
Let me expand a little; all of us (I would think, although we are all different) have an inner monologue that goes on in our head. Sometimes it can be quite angelic encouraging us to not have that extra portion of gelato, while at others it can egg us on to hit snooze and skip the early morning gym part of our routine.
That's pretty healthy.
At times though, our inner voice can be a lot more critical. Especially around communications when we're under pressure; think presentations, interviews and networking events. The our voice can seize on innocuous things and morph reality. Here's an example...
"I was at this networking thing with the APM this evening and I'd had to get the tube at rush hour and I was so sweaty. I was gonna go to the toilet and try to cool down, but this APM guy recognised me and pulled me over to this group, and I swear the two guys on the far side of the circle started laughing when I got there as they found my sweaty forehead hilarious. That just made me more and more embarrassed as I couldn't stop thinking they were laughing at me and I missed their names and then that just made me more flustered and I just couldn't wait to get out of there....."
A more productive, and healthy response would be to have noted the laughing and thought it was some inane joke that they were laughing along with and absolutely nothing to do with me.
So that's what I mean by intra-personal communication; it's how you talk to yourself, especially when you're under pressure.