An important category of data is personally identifiable information, often referred to as P.I.I. or PII, and it's name is suggests accurately what it is: information that can be used to identify an individual person. There are many very familiar examples like name, social security number, address, etc. Some more arcane examples are the sorts of things one needs to supply as a secondary verification of identity at the bank, such as mother's maiden name. P.I.I. is often an explicitly spelled-out regulatory category but there are a number of pieces of information that considered as P.I.I. across jurisdictions and the philosophy defining P.I.I. is consistent even when the level of inclusiveness is not. (Is the name of your first pet personally identifiable information?)
P.I.I. is important privacy is not just about what information is available, but what information can be tied back to an individual. Medical records provide a great example. If someone steals your medical records, this is not perhaps so bad if they lack information to tie these records back to you - from their perspective, they don't have your medical records but only some unknown person's medical records.