Given $y_t=u_t+B_1(u_{t-1})+...+B_k(u_{t-k})=B(L)u_t$, a matrix MA(infinity) process
Response of the $i$'th element of matrix $y_t(y_t)^i$ to a unit shock to $j$'th element of $u_{t-k}$ is given by the coefficient $(b_k)^{ij}$ which is the $i,j\,$th element of the matrix $B_k$. $$ \frac{d(y_t)^i}{d(u_{t-k})^j}=(b_k)^{ij} $$ The assumption on $u_t$ is that they are stationary and independent, which would imply that we can write the above expression as $$ \frac{d(y_{t+k})^i}{d(u_t)^j}=(b_k)^{ij} $$ If you plot $(b_k)^{ij}$ as a function of $k$, you get the impulse response function (IRF)