EGR stands for Exhaust Gas Re-circulation. Its task is to recirculate some of the exhaust gas/fumes back through the engine and result in reducing the emissions from the vehicle. It is and electronic component and commonly gives issues, which is not surprising given the amount of soot and carbon passing through.
A working EGR helps to reduce your fuel costs due to the re-burning of fumes and helps the environment. If your vehicles EGR Valve is faulty, not only will you spend more on fuel, you will probably fail on emissions when you go for an NCT or DOE test.