How to read the block diagram for the 2nd order integrator feedback system?

The wavy symbols are integrators, which means that:

$$frac{dy}{dt} = x_1$$ $$frac{dx_1}{dt} = x_2$$

Then the "+" sign gives you (the triangles are "gains", which means multiply):

$$x_2 = x(t) - a_0 y(t) - a_1 x_1$$

If you combine all this together, you get your differential equation(s).