I'm having trouble understanding what the symbols in this statement mean.

This is the way to determine whether a Boolean Mealy machine is reactive if it helps to provide context, but I'm more interested in what these symbols mean in general because I've seen the same thing elsewhere as well.
Obviously the first part means "for all s that is an element of S", but after that is where it all falls apart for me. What does a disjunction with elements of a set underneath it mean? And why does the disjunction only have one variable (m) on the right of it? What do the square brackets mean in this context?
Can anyone help?