It's obviously from a popular-science book, where the nonsense about "particles moving backwards in time" is unfortunately a common idea to popularize QFT, which cannot be explained with "simple words" but only with mathematics, which is available after a first course on quantum mechanics only. The arrows on the lines of particles indicate flow of charge, and that's why an anti-particle with an arrow pointing into the diagram is in fact an anti-particle moving outward, but that has nothing to do with "moving backwards in time". The in the very few first lectures on relativistic QT you learn that to the contrary in order to have particles only moving forward in time (causality) and at the same time with a Hamiltonian that is bounded from below (to guarantee the stability of matter in the theory) relativistic QT forces you to introduce antiparticles in the very way I described in my previous posting. Dirac came to the same conclusion in a much more complicated way, which shouldn't be taught anymore, because it leads to misunderstandings. My advice to any student of physics is to read a serious textbook about relativistic QFT. A good introductory one is
M. D. Schwartz, Quantum field theory and the Standard Model, Cambridge University Press, Cambridge, New York, 2014.