In terms of games, there are no games that only the pro can play. The PS4 Pro is an enhanced version of the standard PlayStation 4. The same games will run on both models, however there are advantages of playing on the PS4 pro.
The PS4 pro contains a faster CPU and a faster GPU. This allows for better game performance. This comes in 2 forms. Some games will have specific enhancements for the PRO. For example if you play Assassin's Creed Origins on the regular PS4 it will run at 1080p resolution. If you play the same game on the PS4 pro it will run in 4k (in reality it runs close to 1500p). Obviously you need a 4k TV to make any use of this. The reason the resulution is higher is because this game was given a specific update to support the PS4 pro.
In the event that a game has not been given any enhancement for the PS4 pro, there can still be improvements. The PS4 has a feature called boost mode. This will allow the PS4 to use the additional computational power to improve game performance. This typically comes with 2 improvements. The first is a better frame rate and second is faster load speeds. There are of course exceptions to this, but in general these are the improvements you see for non enhanced games.