Agile values are the ideas that describe what Agile development is about. The best way to think about them is as character traits for a person (or company) who wants to be agile.

What is the official business definition of Agile Core Values?

The official business definition of Agile Core Values is:

Individuals and interactions over processes and tools; working software over comprehensive documentation; customer collaboration over contract negotiation; responding to change over following a plan.