In quantum mechanics, bosons are (often massless) force carrying particles like photons or gluons. Fermions are the massive matter particles, such as electrons or quarks.

So, while I’ve never heard this saying before, I assume it’s meaning is that massless particles like photons are best for carrying information around (rather than electrons we are using in circuits today), while the electrons are best for carrying state, like in a switch.

Note, that in networking we have already made that transition by using fiber optics, rather than electric wire to transfer information over longer distances.