Places of Power are stone monuments marked with one of the Signs used by Witchers to combat men and monsters. Drawing magic from these places grants a boost to your Ability Points (increasing by 1) the first time you interact with each monolith. If you come back to a Place of Power and draw from it again, you receive a temporary enhancement to the Sign that is marked on the monument.
The real boon to Places of Power is that they grant this additional Ability Point, which can be spent on new or existing rankings of Abilities (also known as “Skills”) immediately. So it’s worth going out of your way to find all 30 Places of Power across the Northern Realms as early as you can, just to have an advantage earlier in your adventuring.