Some Pocket Nightmares can evolve into more powerful creatures with randomized extra skills.
After their evolution is complete they will also be placed in a new category called "Evolved Pocket Nightmares".
Click a creature's name to reach its status screen, then click evolve to find its menu. The rest should be self-explanatory.
If a Pocket Nightmare does not have this button than its species isn't capable of evolving yet.
A creature must be at least level 50 to evolve. You also need the required amount of an Evolution item mentioned in its Evolution menu.
Remember that not all Pocket Nightmares are capable of evolving.
Random skills a Pocket Nightmare received when evolving are based on its Form. You can read more about those right here.
As an example, this means that an Evolving Zipup, since it's a Wind form Pocket Nightmare, could receive a random mix of its original form Zippit and Jellypeye's skills since they are both Wind form Pocket Nightmares as well.
This also means that as additional Wind Form Pocket Nightmares are added to the game, Zipup's random skill pool will increase in size.