What misregistration is
Registration is how precisely the base colors overlap. When one or more colors are shifted relative to the others, even by a fraction of a millimeter, that's misregistration. How visible it is depends on the artwork: on a photograph it often goes unnoticed, while on small text, thin lines and sharp edges between two colors it's very obvious.
How to recognize it
Typical signs are a colored halo (often cyan, magenta or yellow) on one side of text and outlines, small text that looks blurry or doubled, thin white gaps between two adjacent colors and, in double-sided printing, a front and back that don't line up. A loupe or magnifier shows it clearly: if the color components aren't centered, it's misregistration.
The causes: file or press?
It's not always the file's fault. Mechanical causes come from production: paper that expands or shrinks with humidity, imprecise alignment of plates or print units, irregular sheet feeding and, in digital printing, shifts between front and back.
The causes tied to the file are the ones you can act on: some choices make the defect far more visible, others make it nearly invisible even with a small shift.
What you can do in the file
Use pure black (100% K) for small text, not a black built from several colors: with four colors, the smallest shift blurs it. Avoid small text or thin lines reversed out (light on a dark background) when the background is built from several colors, and avoid very thin lines made of multiple inks.
Where two colors touch, discuss trapping with your printer: a slight controlled overlap that hides any shift. It's often handled by the RIP or the printer, so ask whether they apply it and whether they prefer you to set it up in the file.
Registration marks and printed proofs
Registration marks are small crosses placed outside the finished size, used to check alignment during production. They aren't needed for every digital job: check your printer's instructions on registration marks, crop marks and bleed.
For delicate jobs or large runs, ask for a printed proof and inspect the edges with a magnifier before the run starts.
If the defect is already printed
Compare the print with the PDF you sent. If the colors are centered in the PDF and the defect appears uniformly across several pages or the whole run, the cause is probably the press or the paper: report it to your printer right away with a sample and the PDF. If instead it only affects specific elements (small text in rich black, thin lines), the file may have made it more visible.
Before discussing it, document the defect with close-up photos and keep the exact PDF you delivered.
Common mistakes to avoid
Assuming a PDF that looks sharp on screen guarantees sharp print. Using a rich black for small text. Adding very thin lines built from several colors. Placing small text over colored backgrounds without checking. Not asking for a printed proof before an important run.