Thank you so much for the kind responses.
The only device from which I use to play music is my iPhone. If my computer (where my music files locally reside) is turned off, where does iTunes match draw this information from?
iOS devices stream the music from the cloud, i.e. the iTunes Store. The music in your iTunes library is mirrored to Apple's servers and iTunes Store content is used, except in the case of uploaded tracks. Many people mistakenly assume that by enabling iTunes Match then all the music they play, on any device (iPhone, iPad, iTunes) will come from the cloud. This is not the case, which is why I responded to your "moved my music to the cloud" comment. The music has not been "moved," more like it has been "mirrored."
Also, keep in mind that iTunes Match is not a backup service.