It may be of note that while Dumbledore says this to Harry in the book, it is Sirius who says it to him in the film adaptation.
"The ones that love us never really leave us. And you can always find them... in here."
-Sirius Black to Harry, placing a hand over Harry's heart, before escaping imprisonment on the back of Buckbeak the Hippogriff
I do not personally believe that Dumbledore (or Sirius) meant this literally. However, thematically, there are several occasions on which characters prove that they can be called upon when those who love them are in need. For example, Fawkes is called to Harry's aid in the Chamber of Secrets when Dumbledore is away from the school. Harry's parents also appear and give Harry advice in the graveyard during the Priori Incantatem with Voldemort. They also appear to Harry, aided by the Resurrection Stone, to accompany him on his walk to the Forbidden Forest, where he believes he will die. When he does not exactly die, Dumbledore appears to him again at the ethereal King's Cross Station, to discuss Dumbledore's schemes, Harry's bravery, and what remains to be done to vanquish Voldemort.
It may be of note that while Dumbledore says this to Harry in the book, it is Sirius who says it to him in the film adaptation.
I do not personally believe that Dumbledore (or Sirius) meant this literally. However, thematically, there are several occasions on which characters prove that they can be called upon when those who love them are in need. For example, Fawkes is called to Harry's aid in the Chamber of Secrets when Dumbledore is away from the school. Harry's parents also appear and give Harry advice in the graveyard during the Priori Incantatem with Voldemort. They also appear to Harry, aided by the Resurrection Stone, to accompany him on his walk to the Forbidden Forest, where he believes he will die. When he does not exactly die, Dumbledore appears to him again at the ethereal King's Cross Station, to discuss Dumbledore's schemes, Harry's bravery, and what remains to be done to vanquish Voldemort.
--AK