I am reading Debarre's book, Higher-Dimensional Algebraic Geometry. On page 61, we have the following theorem: if $X$ is a Fano variety of dimension $n > 0$, then through any point $x \in X$ there is a rational curve of $(-K_{X})$-degree at most $n + 1$. In the middle of its proof, on page 62, when Debarre explain the reduction to positive characterist, he says: embed $X$ in a projective space and let $R$ be the finitely generated subring of $k$ generated by the coefficients of the polynomial equations defining $X$ and the coordinates of $x$. There is a projective scheme $Y \rightarrow \mathrm{Spec}(R)$ and a $R$-point $x_{R}$, such that $X$ is obtained from its generic fiber by base change from the quotient field of $R$ to $k$.
My question is: what is $Y$ and how we get the property presented above?
Thank you!