I’m going to try to explain this first with words, then I’ll point to a website that has some decent graphics and some geometrical calculations.
The basic premise in “Slow in-Fast out” is to back the corner up as far as track out is concerned. The idea is while the corner itself can be taken faster using an ideal line, you’re going to sacrifice entry speed, turn-in sooner, push the “apex” later and essentially give yourself an more gradual track-out. This enables you to get back on the throttle earlier (well before the apex), and accelerate faster, thus carrying more speed down the ensuing straight.
I find the turn-in point, depending on the actual corner geometry, may actually go deeper and more to the outside of the corner entry. Instead of carrying speed to the actual corner apex, you brake a bit more slowing the kart down well before the actual apex. This is the “Slow in” part.
You can see in the graphic above the arch is modified from the ideal line. The ideal line would allow more speed to be carried into the corner, but less speed on exit. You can also see how the apex is pushed somewhat later, but acceleration has begun well before the modified apex. The track-out is more gradual allowing far greater acceleration.
Here’s a website with more info and some math. LOL!
Also, it would be beneficial to point out this is best used on corners that empty onto long straights. There are times when its best to be fast in- Slow out. For example at the end of a long straight when the corner connects onto another corner (like an esse) or a small straight followed by another corner. In this case, you may be better off carrying the speed you’ve got on the long straight deep into the corner and sacrificing exit speed. Let the stopwatch be the judge.