Mandrel bending is a pipe and tube bending technique that uses a solid steel rod inserted into the pipe while it is bent. This gives the pipe an even bend without breaking or wrinkling the pipe at the bend. Most commonly a mandrel bend of metal pipe or tube is done on a rotary-draw, pipe-bending machine. A mandrel most often refers to tooling put inside a pipe or tube to help it keep its shape during the bending process.
The best way to look at pipe bending is to compare it to a straight plastic straw. If the straw is completely straight, it's very easy to blow air through the straw due to there being no restrictions. However, let's say you decide to bend the straw 90 degrees into an “L” shape. Now, blowing air through the straw will be very difficult, as the opening at the straw's elbow will have changed from a circle to a very narrow slit. This is exactly how the pipes in your car's intake and exhaust system work.