After any integer is divisible by 3, there must be three situations: divisibility, remainder 1 and remainder 2; Four integers, there must be two numbers divisible by 3 with the same remainder, so their difference must be divisible by 3.

It can also be explained by pigeon hole principle: there are three drawers, and the remainder divided by 3 is 0, 1, 2 respectively. Find any four numbers and put them in the drawer. At least one drawer has two numbers, and the remainder of two numbers divided by 3 is the same, so the difference can be divisible by 3.