Start at 0 and go in both the negative and positive directions. So in the positive one we have 0,1,2,3,4,5,6,7,8,9,19, and keep going forever. Those are the non-negative integers. If we get rid of the o and leave all the others, we have the positive integers.
Now take each positive integer, 1,2,3,4 etc and make it a negative number, so we have -1,-2,-3, etc, those are the negative integers. Or we can start at -1 and count toward negative infinity by going -1, -2,-3, -4, .... forever and those are the negative integers.