It is just a scheme to hold the parameters of the method, just as a general matrix is a scheme to hold the coefficients of a linear map. \begin{array}{c|ccc} \color{red}{c_1}&\color{green}{a_{11}}&\cdots&\color{green}{a_{1s}} \\\ \vdots&\vdots&&\vdots\\\ \color{red}{c_s}&\color{green}{a_{s1}}&\cdots&\color{green}{a_{ss}} \\\ \hline &\color{blue}{b_1}&\cdots&\color{blue}{b_s} \end{array}
If you have seen a general Runge-Kutta method, you should have seen these parameters applied in their correct place, \begin{alignat}{1} \vec k_i&=\vec f\bigl(t+\color{red}{c_i}h, &\vec y&+\sum_{j=1}^s \color{green}{a_{ij}}\vec k_jh\bigr),~~~ i=1,...,s,\\\ \vec y_{+1}&=&\vec y&+\sum_{i=1}^s \color{blue}{b_i}\vec k_ih \end{alignat} So in some sense there is some kind of matrix-vector multiplication done with the coefficients $a_{ij}$.