Understand diagram of a process

I've found this diagram in a slide, but i have no backround to properly understand it. Could you explain to me, in simple terms, how this process behaves and what's the purpose of the blocks $$z^{-1}$$ ?

That's a simple process, where $$y(k)=u(k-3)$$, as the $$z^{-1}$$ blocks just perform a delay by one sample. $$x_1(k)$$, $$x_2(k)$$ and $$x_3(k)$$ are just arbitrary names. In other words: output will be exactly like input, only delayed by three samples.