Mirror is an unlockable Engine Class set with a 150cc speed that "mirrors" all the tracks, making everything on a course flip to the other side (right is left, obstacles on other side, etc.). As if 150cc wasn't hard enough, now you have to drive in basically complete opposite courses of what you just completed in three previous classes. This means driving over edges, crashing into barriers, and running over seemingly misplaced Goombas. Everything, from signs, stripes, and the smallest designs on walls have been flipped. It is definitely as challenging as it can get, as players had just gotten used to them, and now they are flipped.
It can be unlocked by winning the gold trophy in all cups in all Grand Prixes in all Engine Classes (so, yes, it takes a while).
The good news is that the speed remains at 150cc, so it isn't as challenging as it could be. Even so, 150cc is very difficult, and reacting to reversed corners and turns on Mirror mode with the great speed of this engine category is very hard to master.
The computer characters retain the same level of difficulty they had in the previous class... they just seem harder because you probably suck more than the usual un-mirrored tracks. Their vehicles generally go faster than yours, so Items can be very helpful in making sure that they don't get to far ahead.
Mirror mode was first introduced as Extra Mode in Mario Kart 64, with them same mechanics- mirrored tracks. Since then, it's been in every Mario Kart game after that, under the name Mirror or Mirror Mode.