What does the following term means "$\mathbb{Q}$ rationality of ..."

Question

What does the following term means "$\mathbb{Q}$-rationality of a variety" and ". . .variety is $\mathbb{Q}$ rational "

Answer 1

A $\mathbf Q$-rational variety $V$ is a variety over $\mathbf Q$ which is birationally equivalent to a projective space $\mathbf P^n(\mathbf Q)$, i.e. a dense open set in the variety is isomorphic to an open set in the projective space.

This means the field of functions on $V$ is isomorphic to a field of rational functions $\mathbf Q(X_1,\dots,X_n)$.

Answer 2

$X$ is said to be rational over a ground field $k$ if it is birationally equivalent to projective space $\mathbb{P}^n(k)$. For $k=\mathbb{Q}$ we obtain $\mathbb{Q}$-rational varieties.