Suppose given an affine manifold $B$ with potential $K$ and $B$-fields ${\bf B}\in H^{1}(B,\Lambda_{\mathbb{R}}/\Lambda)$, $\check{\bf B}\in H^{1}(B,\check{\Lambda}_{\mathbb{R}}/\check{\Lambda})$. It is not difficult to see, and you will have seen this already if you’ve done Exercise 2.5, that the local system $\check{\Lambda}$ defined using the affine structure on $B$ is the same as the local system $\Lambda$ defined using the affine stucture on $\check{B}$. So we say the pair

$$(X(B,{\bf B},K),\check{\bf B})$$

is mirror to

$$(X(\check{B},\check{\bf B},\check{K}),\bf B).$$