Usefulness of Matrix Notation for Linear Periodically Time Variant Transformations
I don't have the book, so my answer unfortunately cannot be very detailed. However, just based on the excerpt, this could be useful if you are modulating a number of different data streams $\mathbf{X}(u)$ onto a single transmit signal. For example, this would be the case if you have a number of frequency bins that you will use for different data, as would be done for OFDM (orthogonal frequency devision multiplexed) transmissions or DMT (discrete multitone) as is used in DSL modems. I'm personally curious why $\mathbf{h}(t,u)$ is not a matrix and $Y(t)$ a vector, since it is perfectly plausible to have a system with multiple transmitting antennas.