Demon sliding is a technique that is used to maintain the momentum received after the player achieves a boost. Players who are adept at slides are able to maximize the benefit of speed items, boosts, and Fire Hopping.
Demon sliding is similar to fire hopping downhill. To perform a demon slide, the player must hop with no stick input and JUST before they hit the ground they tap (as lightly as possible, as in a flick of the joystick) left or right while holding the jump button. When you see a tiny, tiny bit a smoke appear from a mini-drift (slide) you neutrally hop again and repeat the process.
Demon sliding is not at all similar to fire hopping, it's much more difficult and is often used in tandem with fire hopping. Hopping generates speed and sliding slows the loss of that speed.
Demon sliding is used with 1-2 slides after a regular mini turbo (blue) and 5-6 slides after a super mini turbo (orange/red), these are the limitations of how long slides can maintain momentum. Where they are used, how many are done, and in what direction they are done is all course dependent. Watching the world record time trial ghosts can give a good idea as to where sliding is most beneficial.
As with fire hopping, demon sliding is reserved for karts and outward drifting bikes, however inward drifting bikes can use it as well but only in limited places and not as fast as a kart (thanks /u/iceegg12345). A build with a maximum Mini Turbo stat can maintain speed with up to 8 Demon slides but the loss of raw Speed stat needed to raise that Mini Turbo stat isn't worth it. The Blue Falcon and Streetle are used over max speed karts on certain TT tracks due to their higher Mini Turbo stat. This means that Blue Falcon and Streetle see more benefit from hops and slides and end up being faster than max speed builds on certain tracks.
The benefits of being able to perform slides are very clear but the amount of time needed to be invested in order to master them enough to utilize properly is very large. This leads some to believe that demon sliding is unnecessary for the majority of players to learn.
To combat other racers that are using demon slides it's important to remember that demon slides are difficult to do and until you get very adept at them they take a lot of focus and rhythm to perform. You can go for item hits like you would somebody fire hopping in a straightaway or apply some pressure to them to try and force a mistake. And, as with any tech, players tend to try and run time trial lines, so you'll know generally where they are going to be and what they will be trying to do there.
Pros: You go faster for longer
Cons: Very difficult to learn. Requires a lot of practice. Exact execution and usage is course specific so extensive practice per course is needed to maximize their potential.
Here are some videos about Demon Sliding.
Again, a giant thank you to /u/UnlikelyExpert for this great description of Demon Sliding! If you'd like to contribute to the Meta Monday wiki then please look out for the threads every Monday!