so i can only be used after the big cube's centers and edges are paired up? or is it a method of pairing up the centers and edges?...
Like mentioned before, reduction is reducing it to a 3x3. Sure, big cubes still have 8 corners, like the 3x3, but they have more edges and centers ( a few red/green edges, a few orange centers, etc.) So, reduction would mean putting all those edges and centers together into groups, and then treating each "group" as one unified piece (ex. putting all of those red and green edges together and treating them as only 1 red/green edge) because the 3x3 only has 4 edges per face, and only 1 center. After you finish reduction, you can finish off the cube however you would do a normal 3x3 cube. BUT, on "even" cubes, such as 4x4x4, 6x6x6, 8x8x8, and so on, parity can occur, in the form of 1 flipped edge (not a single flipped edge; a "unified" edge, an edge as it would look like, after reduction), or 2 swapped edges. See
bigcubes.com for a nice tutorial, with animations. Note that the 4x4x4 is called the Revenge, and the 5x5x5 is called the Professor.