What exactly does "carriers of utility" mean?
This expression is used for the arguments of the utility function, that is, for the objects the agent "cares about". In the canonical model, the only carrier of utility is wealth, but in behavioral economics a lot of things can be considered (beliefs, wealth compared to a reference point, ...).

For instance, saying that the carrier of utility for John is the difference between John's wealth and Lisa's wealth means that the utility function of John is of the form $u(x-y)$ where $x$ is John's wealth and $y$ is Lisa's wealth. It is another way of saying that the only thing that matters to John is his relative wealth compared to Lisa, and not his absolute wealth.