Why did the ancient greeks believe that natural places like springs and tree groves were important

That is because every sacred stream, spring, cliff, or tree grove was considered to be invaded by spirits that guarded the areas.

Explanation:

The Celts called areas after gods, or so it has been said time and time repeatedly. Although the folklorist Claude Lecouteux thinks it was a different way around. The Celts described the gods later the sacred places.