When the PS3 launched, we heard all about how it would feature interactivity with the PSP, but in the end, there ended up not being much to it. Here are some of the features that were talked about at the PS3's launch, and what became of them since.
Players would be able to transfer content from the PlayStation 3 to the PSP directly via USB cable, or indirectly by saving the content on a memory stick in the PS3 then moving the memory stick to the PSP. Presumably, you'd be able to transfer content in the other direction, too.
You can transfer content between PS3 and PSP, but since the PSP has its own internet connectivity, there's not really much point.
The PS3 menu features something called "Remote Play". When a PSP is in range of the user's WiFi network, they'll be able to view content stored on the PS3 on the PSP. So if you've got a movie on your PS3 that you want to watch on your PSP, you can watch it without actually transferring the video. As long as you're in WiFi range. You can also access your PS3's menu and other content this way.
Remote Play does work, but the thing gamers were most interested in was being able to play their PS3 games on their PSPs. Very few games support this, and since the PSP only has one analog stick, it's difficult to play those games anyway.
There was the exciting possibility that the PSP could be used in some way as a remote control for some PS3 games. Few game companies actually said much about this option, but it could have lead to some very interesting possibilities. Sony Europe's own racing game Formula One 06 promised to use the PSP as a rearview mirror, which sounded really cool (even though I'm not much into racing games), but I don't think that ever happened.
That, alas, is all there is to PSP - PS3 interactivity. I had hoped it would be more and better, but it was not to be. Here's hoping the PS Vita will do better.