Instant while running (iWR) is a technique to do running moves at close range.
Despite the name, iWR has nothing to do with being fast.
The key to iWR is that the attack button must be pressed exactly one frame after the third f input.
The technique makes use of how the game goes about stopping you from running when the opponent is close. Rather than stopping you from doing a run at all, it simply stops a run immediately after it starts, so there's still one frame where you're in the running stance.
Running moves are powerful. For example, Kazumi's wr2 deals 25 damage with knockdown and wall splats. The only other safe mid she has with better payoff is f,F+4, which is slower, shorter range, easier to step, and worse on block. She also has wr1 which is +7 on block and deals even more damage.
Rather than making running moves fast, the purpose of iWR is to make them consistent. They're at their best at around range 2, but it's possible when you go for one that your opponent does a dash (e.g. a dash block) at the same time. If this happens and you don't do iWR, you don't get your running move.
Even when input quickly, running moves are slow—the input still adds 5 frames minimum to the startup, and more realistically 10+ frames.
iWR does make running moves slightly faster, since you'll be pressing the attack button at the first frame of your run, rather than 2 or 3 frames into it as one might do naturally.
Overusing iWR at close range without a read on your opponent's timing is good way to eat a counter hit, but having the option to use running moves in this situation is also useful, especially when at the wall.
You can buffer the first f of iWR. This makes it faster and thus more of a threat when combined with a big frame advantage. Doing this is a bit harder as now the second f input must also be timed well—exactly as you recover. If you press it too early you'll get the wrong move, and later will be slower.