I don't specifically follow the code itself but I watched the youtube video, and my undestanding is that it takes a 2d array of the previous game board as 0's and 1's, duplicates it 8 times (that's this part: ¯1 0 1∘.⊖¯1 0 1∘.⌽), uses the rotation operators to transpose the arrays left, right, up, down, upleft, upright, downleft, downright, sums the result (this part: +/,) , and runs that through a test for whether the sum in each cell is either 3 or 4 (this part: 3 4=) , turns that into a 1, and returns 0 on all the other cells. the result is the next step.

There's little details in there that I don't quite get due to my unfamiliarity with APL