You're right about what it means. Lenses bend light because of their curved surfaces, and the center points of the curves have to be on the same axis so the bending will be consistent.
It shows up easily via a "star test" on an optical bench, but heck, who's got one of those anymore? (For the bench test, you would have viewed a centered point of light -- generated by a collimator -- as you rotated the lens around its central axis. In a perfectly centered lens, which is rare, the point would stay still. If the lens was decentered, the point would move in a circle, or flare off in various directions.)
Symptoms you might see in pictures include "glowing" highlights (especially if the glow tends to go in one direction more than another, although other defects can cause this too), or an uneven distribution of sharpness.
It's rare for a lens, especially a complicated one such as a zoom, to be perfectly centered, and some designs are more sensitive to decentration than others. So if your lenses seem to be performing well, it's probably not worth worrying about.
On the other hand, if you've (gack!) dropped a lens recently, you might want to have its centration checked as part of a repair evaluation. In traditional lens construction, the individual elements are held in place in machined rings and "cups" that are made of soft metals such as brass or aluminum. A hefty knock can bend these enough to decenter an element, even if no exterior damage is visible. Sometimes a repair technician can repair this damage by carefully straightening the internal mounts; I once had a 135/2.8 Komura lens in Leica thread mount that was almost unusable when I got it, but improved amazingly once it was straightened.