Unlike the PlayStation 4 Pro, which supports 4K gaming, the slim PlayStation 4 will only support HDR gaming for those that have HDR-capable televisions.
In the near future, Sony will release a firmware update for all PlayStation 4 models (including older models) that will make them HDR-compatible.
If you're not familiar with the term HDR, it's a feature on certain high-end televisions that stands for "high-dynamic range imaging." Essentially, it means that the range of colors the television can display is far greater than that of a normal television.