Basically, empirical evidence is info gathered from experiments and observations. So what they mean is, in order for it to be a theory they need to have some sort of research or experiments to back it up.
Stating that a scientific theory must be supported by empirical evidence means that the theory must be supported by testing it out through research. If research results demonstrate that the psychological claim has been backed by data in a significant manner then accuracy for the theory is established and the theory is said to be backed by empirical evidence.
