Alan Hull's construction takes a weighted average of half the period, doubles it, subtracts a weighted average of the full period, then smooths the result over the square root of the period. The subtraction is what removes most of the lag.
The line is visibly smoother and faster than an equivalent exponential-moving-average, which makes it popular for trend colouring and for visual regime reads.
The cost is real and often unstated. Because the construction extrapolates, the Hull average can overshoot at turning points and can change the direction it displayed on the most recent bar as new data arrives, which is a mild form of repainting. Backtests that use its colour naively will overstate results.
Related: weighted-moving-average, exponential-moving-average, repainting, indicator-lag, supertrend