Bleed is the most misunderstood problem by many designers when sending a job to a commercial printer. To a commercial printer it is very important.
So make your art around 3 mm bigger on each side, (if it has color going right to the edge).
The printed paper (or card) will be placed in a stack and the bleed will be trimmed off by your commercial printer in the guillotine.
If you don't add bleed there may be small white areas showing up on the edge of the paper when guillotined.
However usually a good commercial printer will check if it has bleed before printing. If there is a problem (no bleed) he may be able to fix it or more than likely ask you to fix the art. Sometimes it may be difficult for the commercial printer to fix the art, particularly if there is a pattern or photograph at the edge, so that's why it is better for you to fix.
Also make sure any text is kept away from the bleed edge, (or it may get trimmed off in the guillotining process). I like to keep text in around 3 mm from the bleed edge. (Which is 6 mm from the outside edge where the bleed was added).
Understanding bleed will resolve on of the biggest in artwork that commercial printers face.