Auditor independence
In one sentenceThe auditor being free of any interest in or relationship with the business that could affect his impartiality, so that his opinion on the statements is reliable for those who read it.
Simply put
The whole value of an auditor's report lies in his independence: if he is a partner or relative of the business owner, or keeps its books, the bank or investor will not trust his opinion.
Independence has two sides: independence in fact, in the auditor's thinking, and independence in appearance, so others see nothing that would cast doubt on it.
Example
An accounting firm prepares the financial statements of a trading establishment and keeps its books all year, and is then asked to audit those same statements: here it would be reviewing its own work, which affects its independence.
Don't confuse it with
Professional skepticismAn auditor may be independent yet accept evidence without scrutiny, so both are required together.