The cash flow news / discount rate news decomposition is given by
$$r_{t+1}-\mathbb{E}_t[r_{t+1}]=(\mathbb{E}_{t+1}-\mathbb{E}_t)\sum_{j=0}^{\infty}\rho^j\Delta d_{t+1+j}-(\mathbb{E}_{t+1}-\mathbb{E}_t)\sum_{j=1}^{\infty}\rho^j\Delta r_{t+1+j},$$
where $r_{t}$ is log-return $d_{t}$ is log-dividend and $\rho$ is a constant. This follows directly from the Campbell-Shiller decomposition.
Here the second term is discount rate news that determines shocks to the path of expected log-returns. This will be zero if expected stock returns are constant as in older finance theories. On the other hand, it is generally non-zero if returns are predictable. To see this assume we find $\beta\neq 0$ for some predictor $x_t$ so that
$$r_{t+1}=\alpha +\beta x_t+\epsilon_{t+1}.$$
Then the discount rate news component is
$$(\mathbb{E}_{t+1}-\mathbb{E}_t)\sum_{j=1}^{\infty}\beta\rho^j\Delta x_{t+1+j}$$
For simplicity assume the predictor is AR(1) with persistence $\lambda$.
$$(\mathbb{E}_{t+1}-\mathbb{E}_t)\sum_{j=1}^{\infty}\beta\rho^j\Delta x_{t+1+j}=(x_{t+1}-\lambda x_t)\frac{\beta\lambda\rho}{1-\rho\lambda}.$$
Hence return predictability implies that return variation is partly driven by discount rate news. Modern asset pricing theories try to explain why certain variables $x_t$ can forecast returns. In the habit model the key predictor is consumption growth so higher consumption means lower expected returns. This can also explain why price-dividend ratios forecast returns. In the long run risk model there are two predictors: expected consumption growth and consumption volatility.
The cash flow news component does not create return predictability but creates variance in returns as a positive shock to future cash flows leads to higher returns.
