Answer
Possession in the concept of an owner is possession under a claim of ownership — the possessor holds the property as if it were his own. Possession in the concept of a mere holder is possession while acknowledging that ownership belongs to another, as with a lessee, depositary, or agent. The distinction matters because only possession in the concept of an owner can ripen into ownership through acquisitive prescription; a mere holder can never acquire ownership no matter how long he holds, unless he clearly repudiates the owner's title by unequivocal acts made known to the owner.
This also drives the classic dispute over possession by tolerance: a person who occupies land merely on the owner's tolerance is a holder, not an owner, so his stay never ripens into ownership, and it becomes unlawful — the basis for an unlawful detainer suit — once the owner demands that he leave and he refuses. In any event, Torrens-registered land is generally immune to acquisitive prescription (Section 47, Presidential Decree No. 1529).