Consider $R^{r+s}$ associated to quadratic form $q=\sum_{1\leq i\leq r}x_i^2-\sum_{1\leq i\leq s}x_{i+r}^2$. Then one can associate $Cl_{r,s}$ Clifford algebra to $R^{r+s}$. There is twisted representation $Ad:Cl_{r,s}^\star\to GL(Cl_{r,s})$ where $Cl_{r,s}^\star$ is the set of invertible elements of $Cl_{r,s}$. Now $Pin_{r,s}$ pin group and $Spin_{r,s}$ spin group are subgroups of $Cl_{r,s}^\star$ which restricts the representation to $Pin_{r,s}\to GL(R^{r+s})$ and $Spin_{r,s}\to GL(R^{r+s})$. Furthermore, the restricted representations has image in $O_{r,s}$ and $SO_{r,s}$.
"... the algebra $Cl_{r,s}$ contains groups $Spin_{r,s}, Pin_{r,s}$ and so any representation of algebra $Cl_{r,s}$ restricts to representation of these groups which is non-trivial on the element $-1$.(Such representation are therefore not induced from representations of $O_{r,s}$ or $SO_{r,s}$.)"
$\textbf{Q:}$ What is induced representation of $O_{r,s}$ or $SO_{r,s}$ here? $Pin_{r,s}\to O_{r,s}$ is surjection with $Z_2$ kernel. In particular, $Pin_{r,s}$ is not subgroup of $O_{r,s}$. It should not mean standard "induced representation on subgroups". I guess the context is saying that $Pin_{r,s}\to GL(V)$ s.t. image does not factor through $O_{r,s}$.
Ref. Spin Geometry, Chpt 1, Sec 3