Sapience is reached when a being has reached human-like brain capacity. It shows that the being is able to think for itself and reach conclusions to complex problems.
Significance in Tolkien Mythology
The Ainur, being direct offshoots of Eru‘s thought are most certainly sapient beings of a high order. Sapience is bestowed upon all the Children of Ilúvatar by which they have the ability to govern their own lives in fulfillment of Eru's plan.
Sapience comes from the Latin word sapiens (wise) which is also the source of the scientific name for humans, Homo Sapiens.