An independent personal pronoun is a personal pronoun that is a free form.
An alternative term that is often used is "free personal pronoun". Since personal pronouns in English, German and Russian are always free, the modifier "independent" is very often omitted. One also often sees "personal" omitted ("independent pronoun"), which makes sense because only personal pronouns make a frequent distinction between independent and bound forms. The definition here is not in terms of "separate word" (as in Siewierska 2004: 16), but in terms of "free form".