It is one of Dean's most prized possessions.
The photograph fell into Dean's possession at an unknown point and became one of his few tangible memories of his mother, who had been killed around the time this photo was taken.
Upon moving into the Men of Letters bunker, Dean kept the photo in his room. He would switch between leaving it on the nightstand, in a trunk, or in a drawer. At one point, he framed the photo. It is also possible that Dean has multiple copies of this particular photograph.
When Eldon Frankenstein planned on setting aflame a box of Dean's things, this photo was likely among the collection. Dean's things were spared from being destroyed by the timely arrival of Dean himself.
When Death ordered Dean to kill his brother Sam in exchange for his help in dealing with the Mark of Cain Sam shows this photo and another photo to Dean as a guide to remind Dean, some day, what it was to be good and what it was like to love. This causes Dean to not kill Sam and instead kill Death.
The photograph played a major role in the resurrection of Mary Winchester. When the Darkness discovered the bunker's location and searched through Dean's belongings, she found this photo inside a trunk and may have realized that Mary was someone Dean missed and held dear.
Upon reconciling with God with the help of Dean, The Darkness chose to resurrect Mary for she was something he wanted. Mary herself would eventually see the photo, more than three decades after it was taken.
When Arthur Ketch and his henchmen infiltrated the bunker, Arthur searched Dean's room and discovered this photo in the drawer. He subsequently took it back to his workplace at the British Men of Letters compound for reasons unclear.
This particular copy or the photograph itself was likely destroyed when American hunters led by Sam destroyed the compound.