Nexus 6 Replicants don't have implants, they are aware of their condition as artificial beings and the only memories they have are the ones they make in their short lives. So they become obsessed with registering memories.
In the theatrical version Deckard's narration tells that he is puzzled by the replicant's obsession with photos and states
Leon's photos had to be as phony as Rachel's
but finds out later that they're not fake, and where taken by Roy's group, probably by Leon himself. They are the reason Leon goes back to his apartment.
Since their life span is so short and they don't have a past, they cling to their precious few memories, and as they'll be lost soon, they're a proof of their life experience.
All those memories will be lost in time
To Rachel they have an added significance, because she does have implanted memories of a childhood, and her attachment to the photos is not only for the past they represent, but as a reaffirmation of her humanity that she fears not having. As Tyrell states earlier when Deckard says she doesn't know:
She's beginning to suspect
The writings in the back of the photo show how careful Tyrell was when giving Rachel a past, as Deckard thinks "Tyrell thought of every detail", and why Rachel chose to carry it.
The photos are also a source of suspicion for the viewer, before the Final Cut Edition. Seen as how Deckard's apartment is so abundant with old photos, it was another indication that he could also be a replicant.
