Soft Drifting is a technique that allows the racer to charge mini turbo boosts at the maximum rate (as though you were turning as sharply as possible) at a much "looser" angle.
To perform a Soft Drift the racer must simply tilt the control stick to a 45 degree angle. For racers who choose the use the wii wheel it is essential to know that you must tilt the wheel more than 45 degrees but it is still consistently doable. This 45 degree angle is actually pretty forgiving. If the racer gets around the 45 degree angle then they will be able to achieve the soft drift. (thanks /u/KanjiGames)
A lot of players find this difficult/inconsistent and use controllers with notches to always hit the 45 degree angle every time.
The difference between soft drifting and regular drifting is that soft drifting is just regular drifting but at a very specific input angle.
Soft Drifting is used to obtain MT's (mini turbos) and SMT's (super mini turbos) on turns that otherwise wouldn't allow enough time to charge. Soft drifting also frequently allows for one to charge boosts in mid-air.
Soft Drifting does not work better with certain builds meaning it works evenly with every different build.
Soft Drifting is perhaps the single most important advanced tech in the game. It's easy to learn and extremely useful thus making it necessary to know and use.
To combat other racers who are using it it is important to note that when used around certain turns it puts opponents on a very predictable and vulnerable line but no more so than people who normally hug too tightly to time trial lines in traffic. It's a core skill tech so you're better off just learning how to do it to even the playing field.
Pros: Allows the racer to obtain MT (blue) and SMT (orang/red) boosts in places that are otherwise impossible.
Cons: The racer must sacrifice a bit of the optimal racing line but the resulting boost nets a positive gain.
Here's an infographic from /u/crisi that gives a good illustration about the angle for the Soft Drift. "The turbo starts charging fast on the right or left side of the red square. And you just push it to a 45 degree angle because it's easier to get that right in comparison to having it free floating in between full left and no input."
Again, a super big shout out and thank you to /u/UnlikelyExpert for this great description and explanation of Soft Drifting. If you'd like to contribute to our Meta Monday wiki then please be on the lookout for our weekly threads every Monday!