4x4 parity occurs on the last layer of a 4x4, where you get a case that is impossible to get on a 3x3 so you need a specific algorithm to solve it. OLL parity specifically occurs because two adjacent edge pieces are flipped, but generally you can't recognize it until you are at the OLL stage of solving.
OLL Parity Algorithm 1:
This algorithm is the easiest to execute. It flips the two edge pieces as well as the corners. It also moves other edge pieces in the top layer. If your focus is speedsolving the 4x4 then this is the recommended algorithm. This should be done before you permutate the corners and edges of the last layer. If you are using CFOP then this is done at the OLL stage, hence the name (OLL Parity).
Rw U2, X, Rw U2, Rw U2 , Rw' U2, Lw U2, Rw' U2, Rw U2, Rw' U2, Rw'
OLL Parity Algorithm 2:
If you have completed your 4x4 solve and you only want to flip the 2 inner edges then you can perform the algorithm below. It is slower to execute, but will not disturb any other pieces.
r', U2, l, F2, l', F2, r2, U2, r, U2, r', U2, F2, r2, F2
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|Rw||BOTH Right Layers|
|r||INNER Right Layer|
|Uw||BOTH Top Layers|
|u||INNER Top Layer|
|X||Turn the cube clockwise around the X-Axis|
|X'||Turn the cube anti-clockwise around the X-axis|