This is the context:
Again, the importance of fine-tuning turns on how narrow or how broad the tolerances around fundamental constants, while still being consistent with the formation of stars and planets, and with sufficient time, for the generation and evolution of life.
What is the meaning of "turns on"? Does it mean "revolve on an axis or hinge"? and does the bold "around" is attached to turns on? And another question, why in the last part of the sentence there is no verb? does it mean to be "consistent for"?