[Update: according to information in the official press release you still need to own the original UMD. The 'free play' bit refers to the fee you used to have to play to transfer the game to Vita. Looks like that bit got screwed up in the previous translation. Very sorry about that.]
The PSP's Passport program originally let you effectively transfer ownership of your old UMD games digitally onto Vita. In what looks like an experiment, much of the back catalogue, around 250 games*, will be available for free to PS Plus subscribers in Japan, starting September 17th and lasting the rest of the year.The program is Japan only at the moment reports Siliconera, but what starts over there usually comes over here eventually.
[*UPDATE: Apparently there are around 370 games in the Japanese UMD PSP Passport library so it's most, not all of them.]