A reflexive possessive pronoun is a special case of a possessive pronoun, denoting that it is the subject of the sentence who possesses the object. It does not exist in English, which uses "his own/her own etc." to cover the concept.

Let me clarify:

In English, we can say, "John has a book. Fred takes his book."

Unfortunately, we don't know whose book Fred is taking, although it's likely from the context that it's John's.

In Swedish, for example, the reflexive possessive pronoun is explicit, viz:

"Sven har en bok. Åke tar sin bok." - "Sven has a book. Åke takes his (Åke's) book."

Compare with the non-reflexive version:

"Sven har en bok. Åke tar hans bok." - "Sven has a book. Åke takes his (Sven's) book."

(Carthag points out that this exists in other Scandinavian languages, as well as German, and probably others.)