When something is ostensible it appears to be the case but might not be. Your ostensible reason for visiting every bakery in town is that you're looking for a part-time job — but I think you really just want to eat cupcakes.
Just because something is ostensible doesn't necessarily mean that it's not as it appears to be, only that there's a possibility of another reason. Your ostensible reason for calling your crush was to ask about homework; the real reason was that you were hoping they would ask you out. Ostensible derives from the Latin verb ostendere, meaning "to show or display."