Parity?

[Awkarden]

I got a 4x4 and I was wondering why there is parity on any cube.

 

[shadowslice e]

Parity occurs when a "mistake" is made in the reduction phase and the cube is reduced to a state (say C*) which cannot be solved using 4x4 outer layer moves as there is no way for those operations to transform the state from C*->C. Thus they must be transformed using wide moves or slice moves.

In more basic terms, there are 2 2-swaps (1 of wings and 1 of centres for OLL IIRC and 2 of wings for PLL) which can only be changed using a parity algorithm.

 

[newtonbase]

You have pairs of pieces that look the same but are not the same. If they get switched then you have parity.