ما معنى Forward smile؟

The forward smile from $t_1$ to $t_2$ is the implied volatility, as a function of the relative strike $x$, of forward-start options that pay $(S_{t_2}-xS_{t_1})^+$ at $t_2$: the smile that the model expects to see at $t_1$ for options of maturity $t_2-t_1$.