This means "NEO Mode" can offer higher or more stable frame rate and other visual flourishes. "The NEO will also support 4K image output, but games themselves are not required to be 4K native." In Sony's developer guidelines documents, the company reminds that games can't push 4K on the NEO at expense of performance. "Sony repeatedly reminds developers that the frame rate of games in NEO Mode must meet or exceed the frame rate of the game on the original PS4 system."
There will be no NEO-specific games (as with the New 3DS, though it's rarely been the case), as "Sony explicitly and repeatedly states that developers cannot offer exclusive gameplay options or special unlockables for NEO players." That said, NEO can offer improved versions of existing features; the example offered is a four-player local co-op PS4 game could theoretically offer eight-player local co-op on NEO. Given Sony's strict rules in keeping from splitting PS4 ownership, though, I doubt this will come up too much.
Similarly, all PS4/NEO games must have peripheral parity, so VR modes can't be locked to NEO. This means, contrary to the initial idea that NEO is specifically meant to accommodate VR, that your NEO can only be better at VR on a technical level. Also, despite games as early as September needing to be NEO ready, "devs are allowed to launch NEO-ready games before the NEO itself releases," so this doesn't confirm a launch alongside PS VR, at least not on its own. Existing PS4 games can also be patched to allow for NEO versions with better performance, but I don't expect a lot of developers taking advantage of the option. It took four years for Metal Gear Solid 4 to get Trophy support.