This is a page from "Fundamentals of Musical Acoustics", by Arthur H. Benade. This diagram is a floor-plan view of a room, with a sound source (the red dot) and a listener (the green x). The diagram is showing how the listenener hears the sound come directly from the source, as well as from the walls that it bounces off of. Since the sound bouncing off of the wall has to travel further, it reaches the listener after a slight delay. I've added in blue how reflecting the position of the sound source across the wall makes the sound travel the same distance as if the sound had bounced off of that wall.
A listener would hear lots of these bounces happen very quickly, each one adding a copy of the sound with a slight delay. To visualize this, I created diagrams like the one above, but reflected the sound source across the walls many times. In the image to the right, for example, the gray rectangle is the shape of a room. The rows of reflected sound sources (the red dots) would form echoes. If you've ever clapped your hands in a long hallway, you've probably heard this happen.
Visualizing rooms of different shapes led to a few insights. In the image at the top of this page, the room is in the shape of a narrow triangle. I didn't expect this to create echoes or anything, but it seems that it would, since the dots form concentric circles around the listener. In the image to the right, I tried an octagon-shaped room. I thought an octagon would aproximate a circular room, which would cause lots of echoes, but the dots get scattered pretty quickly here, so there probably wouldn't be any strong echoes.
I also ran across this image on this site. I need to find out more about the book it was taken from, but it illustrates the way reflections work pretty well: