What does this equation mean?

Stated formally, the bound says that for two operators $A_x$ and $B_y$ acting on well-separated lattice sites x and y , the size of their commutator after evolving one of them forward in time t is capped by an exponential in the distance between the sites minus the cone’s own reach: $\lVert [A_x(t), B_y] \rVert \le C\, e^{-\left(d(x,y) - c_{\mathrm{LR}}\, t\right)/\xi}$. where C and $\xi$ are constants fixed by the microscopic couplings and d(x,y) is the distance between the two sites on the lattice [ 1 ] . Outside the cone, where d(x,y) exceeds $c_{\mathrm{LR}}$ t , the right-hand side collapses toward zero; inside it, the inequality simply has nothing to say. The velocity $c_{\mathrm{LR}}$ plays exactly the causal role the vacuum speed c plays in relativity, with one difference that matters for everything that follows: it is a property of the material, not of empty space, and it changes from one lattice to the next.