Boundary conditions

Explain why the following two boundary conditions must hold at the point $x=0$,

$$y_0(x=0,t) = y_1(x=0,t)$$ (2)

$$\tau \left. \frac{\partial y_1(x,t)}{\partial x} \right\vert _{x=0} - \tau \left. \frac{\partial y_0(x,t)}{\partial x} \right\vert _{x=0} = m \left. \frac{\partial^2 y_1(x=0,t)}{\partial t^2} \right\vert _{x=0}.$$ (3)