I have recently learned this algorithm, so excuse me for my poor explanation.(and my poor English :D)

consider we have a string S and we want to sort all suffix of S in O(nlgn * lgn).

first of all we add some extra character to the end of S that they're maximum character in our alphabet.

then for every j (1 <= 2^j < 2^k) such that 2^k is first power of 2 that's larger than size of S and every i (0<= i < size of S), we will sort all substring of S that starts from i and they're length is equal 2^j in O(nlgn).

consider (i, j) a substring of S that starts from i and it's length is equal 2^j

in each step(for every j) we spot a number from 0 to n-1 for every substring (i, j), that it's position in all substrings (i, j). we call this number D[i][j]

we can calculate D[i][j+1] in this way :

1 . for every i : D[i][j + 1] = (D[i][j] * n) + D[i + 2^j][j]

2 . sort all D[i][j + 1], and then change value's to numbers from 0 to n-1 (as explained above).

the total complexity is equal O(nlgn * lgn).

I know there's a O(nlgn) algorithm but I have no idea for that one :D