A very simplistic explanation is this....A triple bypass is where 3 blood vessels must be mended and a quadruple, 4. Bypass meaning those particular arteries have build-up (clogged) and are ineffective in blood transport for the heart. Typically, an artery is taken from the leg and the passageways are reconstructed in those areas around the heart, effectively "bypassing" the clogged artery so blood can flow as it was meant to.
There are two main arteries that come off the aorta to feed the heart: left and right. The left one breaks into several smaller arteries (circumflex, anterior, diagonal, among others). The image at left shows the major arteries. If these get clogged, the heart isn't able to pump blood to itself. That's an infarction, and the heart muscle itself begins to die. Then you die. So, we can bypass the clogs. We take a chunk of vein, such as from the leg, and simply route around the bypass. "Simply", of course, is relative, since you're trying to make pressure-tight seal on a pump which is still working. Or they stop the heart to do the work, and I wouldn't call that "simple", either. But you get the idea. "Triple" and "quadruple" is just counting how many bypasses they have to do. Usually, "quadruple" means one on each of the four major arteries, but it depends on precisely where the clogs are. You can even get quintuple bypasses, bypassing some of the other branches.