The informal definition of P.I.I. (personally identifiable information) is plain - it is information that can be used to identify an individual person. It is important, though, that this informal definition is a bit fuzzy around the boundaries and P.I.I. is also a formal regulatory category defined differently in different jurisdictions.
For example, in the United States the NIST defines P.I.I. as "any information about an individual maintained by an agency, including (1) any information that can be used to distinguish or trace an individual's identity, such as name, social security number, date and place of birth, mother's maiden name, or biometric records; and (2) any other information that is linked or linkable to an individual, such as medical, educational, financial, and employment information."
On the other hand, the European Union's General Data Protection Regulation does not utilize the concept of P.I.I. but rather the more inclusive concept of "personal data" which includes all information about an individual whether it can be used to identify them or not.