Viruses: Adaptation to a new host through repeated host jumps
A friend told me, during a 3 minute discussion, that viruses that are
  endemic in host A and make repeated jumps to host B but can't be
  transmitted between individuals of species B, may slowly adapt
  (through these repeated jumps) to be able to be transmitted between
  individuals of host B and become epidemic.


This is...mostly true. A good example is avian influenza - there are a number of human infections linked to contact with infected poultry, but the virus is not particularly good at sustaining long chains of human-to-human transmission, likely due to differences in the respiratory tract between humans and birds.


  I don't know much about epidemiology. I don't understand how a virus
  population that is endemic to host A may adapt to host B with repeated
  jumps while the viruses that jump to host B are dead end because they
  cannot be transmitted further more. Or Are these viruses able to jump
  back to host A to bring back their newly acquired adaptations to host
  B?


What they mean by repeated jumps, or what they should mean, is not a virus hopping back and forth, but a virus going from A to B many times. This is my problem with your friend's statement, it's not so much a "slow adaptation" as, well, random chance.

Imagine that there's a mutation in Virus A, which lives in chickens, that will make it well adapted to live in human beings. It's an extremely rare mutation, so the dominant strain of Virus A is maladapted for human to human transmission. That means most Virus A infections in humans will be the non-productive kind, that will infect a person, but not go on to infect other people. But, with enough rolls of the dice, a human might get the human-favored Virus A, and since there's now intense selective pressure for that strain of the virus within its new human host, it might establish itself and take off.