Following is an attempt to explain +/((⌽⌈\⌽a)⌊⌈\a)-a

The functions ⌊ ⌈ find min and max values, and \ is functional programming scan operator. Combining ⌈\ gives max-scan which does this:

          twentyRandoms
    71 61 79 72 84 76 76 88 16 53 51 56 64 50 100 33 60 82 96 53

          ⌈\twentyRandoms
    71 71 79 79 84 84 84 88 88 88 88 88 88 88 100 100 100 100 100 100

moving to the right, the largest value (max) seen so far is kept and carried on.

Then ⌽ reverses the values in an array so this (⌽⌈\⌽a) does the same thing going from right to left, by reversing, max-scan, then reversing the result:

          twentyRandoms
    71 61 79 72 84 76 76 88 16 53 51 56 64 50 100 33 60 82 96 53

          (⌽⌈\⌽twentyRandoms)
    100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 96 96 96 96 53

Then the ⌊ in the middle compares the two results an item at a time, taking the minimum of each pair:

          (⌽⌈\⌽twentyRandoms)⌊⌈\twentyRandoms
    71 71 79 79 84 84 84 88 88 88 88 88 88 88 100 96 96 96 96 53

The (...a) - a part does item by item subtraction, each number in this result array minus the number in that position from the original array.

          ((⌽⌈\⌽twentyRandoms)⌊⌈\twentyRandoms)-twentyRandoms
    0 10 0 7 0 8 8 0 72 35 37 32 24 38 0 63 36 14 0 0

Then +/ sums them up like a sum() or foldr or reduce:

          +/((⌽⌈\⌽twentyRandoms)⌊⌈\twentyRandoms)-twentyRandoms
    384

Which, if I remember the talk and the code works, means that if you drew this array as a bar graph and poured water into the top middle of it, how much water would it hold before it all overflowed? The highest block on the left and the highest block on the right are the bounds of the highest points where the water can't get past. In between those, the bar heights are the depth at each position, and the water depth is from there up to the lower of the highest bar.