It does explain it...
What you do is, you switch on each of the five rows in turn, and read the eight columns. From that you can tell which keys are pressed. You scan through the five rows very quickly and at a steady rate, so that there isn't a noticeable delay between pressing a key and the note sounding.
So, in your microcontroller you have a timer set to fire an interrupt every 1/1000th of a second (for example). Every time the interrupt fires, you read each key as quickly as possible (actually twice, because you want to debounce the keypresses, but ignore that for now). Put every key that's pressed on a list, and remove any keys that are no longer pressed from the list. Depending on which key you want to have priority, decide which note you're actually going to play. For a "classic" monosynth keyboard, take the highest key that's pressed. For a "classic" polysynth keyboard, take the most recent N notes where N is however many voices your synth has.