Decentering is when an element (or more than one) doesn't have its optical axis quite perfectly aligned with the others. Decentering is really a matter of degree -- every lens element is decentered to at least some degree. All that's open to question is whether it's severe enough to cause a real problem.

Depending a little on what element is off center, the result is normally that the sharpest part of the picture isn't at the center, and (usually) the fall-off in sharpness isn't entirely symmetrical. Typically it shows up as one corner being sharper than another.

This is one if those issues that's often rather exaggerated in many lens tests. When you shoot a large target that's entirely flat and has lots of detail right out to every corner, it can be pretty obvious when one corner is sharper than another. When you shoot mostly 3D targets and the corners are rarely in perfect focus, you could easily shoot a lens that was pretty badly decentered for years and never have a clue anything was wrong at all.