The EGR recycles exhaust gases back into the air intake to reduce NOx emissions. (not measured on the MOT).
It also causes oil mist in the inlet gases from the engine breathers to be turned into a tar like mud that can clog up the intake manifold and ports. A substantial amount of this can be present in the car with no apparent performance defects (as the tar will only settle in low velocity areas).
People believe that stopping this buildup of tar is beneficial for performance in the long run.
However the buildup is a slow one so you’ll not see a benefit (if there is one) for many 10’s of 1000’s of miles.
If the EGR goes faulty then it leads to poor performance and excess smoke.
If you disable the EGR your engine takes marginally longer to warm up.
To bypass the EGR you can use several methods however on post 2004 cars bypassing the EGR will cause the engine management light to come on.