Private key is numbers that allow users to access their funds, sign transactions and to generate receiving addresses.
A private key is akin to a secret PIN or check signature that gives you authority over your account. Users of bitcoin are rarely exposed to these digital keys. They are saved in the wallet file and controlled by the bitcoin wallet software for the most part. It is usually written as a long string of letters and numbers.
Example of private key: 1J7mdg6rbQyUHENYdx39WUWK7fsLpEoXZy KxFC1jmxxCoACiCAWZ7eXa96mBM6tb3TYzGmf9YwgdGWZgawvrtJ