That means : $\cal D $ has $n$ éléments $z_1,\cdots,z_n$ having the form: $$z_i=(x_{i,1},x_{i,2},\cdots,x_{i,p},1)$$ or $$z_i=(x_{i,1},x_{i,2},\cdots,x_{i,p},-1)$$ where $x_{i,1},x_{i,2},\cdots,x_{i,p}$ are real numbers.
If we want, we can represent this by a matrix :
$$A_{\cal D}=\begin{pmatrix} x_{11}& x_{12}&\cdots& x_{1p}& \varepsilon_1 \\ x_{21}& x_{22}&\cdots& x_{2p}& \varepsilon_2 \\ x_{31}& x_{32}&\cdots& x_{3p}& \varepsilon_3 \\ \vdots &\vdots&\cdots&\vdots& \vdots \\ x_{n1}& x_{n2}&\cdots& x_{np}& \varepsilon_n \\ \end{pmatrix} $$
Where $\varepsilon_i=1$ or $-1$ for all $i \in \{1,..,n\}$
We can now see elements of $\cal D$ as lines of the matrix $A_{\cal D}$.