Meaning of "next greater permutation"?


#1

What exactly is the meaning of this phrase “next greater permutation” used in the question? How can a permutation or sequence of numbers be compared to another?


#2

Lets assume an array [1 2 3]. Its next greater permutation is [1 3 2] followed by [2 1 3] and [2 3 1]. These are the possible permutations for this array where every permutation is the next greater permutation of the previous permutation:
[1 2 3]
[1 3 2]
[2 1 3]
[2 3 1]
[3 1 2]
[3 2 1]