From top to bottom, the values are:
-2, -1, 0, 1, 2
You can use a graphing calculator to have a function y = x^(1/3) and see what the y values are for the particular x values shown. Alternatively you can compute each input to get (-8)^(1/3) = -2, and (-1)^(1/3) = -1 and so on. The exponent of 1/3 is another way of writing cube root.
The cube root is the opposite of cubing something. If we go from 2 to 2^3 = 8, then reversing this has us go from 8 to 2. Think of a block of clay that is 2 by 2 by 2. The volume of this block is 8 cubic units. If you want to find the side length, then you would apply the cube root (or do guess and check).