Free monsters are the ones you add to your team that is not a partner to one of the main characters.
To evolve a free digimon you must collect a mature enlightenment slab from a shrine that can be used on them by selecting the digimon under status, tabbing over to evolution and selecting the evolution you want (if there’s more than one option).
The first slab can be found in the Inner Shrine of the first area, part 2 of the story.
These items will become much more common as you progress through the game.