A handclap in a hard room does not die away. It is reflected off every surface and comes back, and the sum of all those arrivals is the room's fingerprint. A cathedral gives you two seconds of it; a bedroom gives you a fifth of a second. The difference is how much energy the walls swallow.
The image source method replaces the reflections with pictures of the source. To find where a reflection comes from, mirror the room in the wall it bounced off and put a copy of the source in the mirror; the straight line to that copy is the path the sound took. Repeat for every wall and you get a lattice of images, and the whole reverberant field is the sum of the straight lines to all of them.
Each image carries a delay equal to its distance divided by the speed of sound, and an amplitude equal to the reflection coefficient raised to the number of reflections it has made, divided by the distance. The result is a list of arrivals — and that list is the impulse response you can hear.
The clap on the page is a real sound, and it is convolved with the computed impulse response of the room you have built, so the audio and the drawing come from the same maths. Change the absorption and the tail gets shorter; change the size and the delays spread out.
The reverberation time is the time for the sound to fall by sixty decibels, and Sabine's formula says it is about 0.16 times the volume divided by the total absorption. That is why a big empty hall is a bad place to hear a violin and a small panelled room is a good one.