Reduction modulo lattice parallelepipeds

Question

I was checking the following lecture notes, and on page 5, it says that $m$ vectors $x_1,\ldots,x_m$ are independently sampled from the Gaussian distribution, and then they are reduced modulo the parallelepiped $\mathcal{P}(B)$ of the lattice $\Lambda(B)$, where $B$ is the basis, in order to obtain new vectors $y_1,\ldots,y_m$. Given that the parallelepiped is defined as $\mathcal{P}(B) = \{ \sum a_ib_i \mid a_i \in \mathbb{R}, a_i \in [0,1) \}$, what exactly it means to reduce a vector modulo the parallelepiped, i.e., compute $y_i = x_i \mod \mathcal{P}(B)$?