Bleed is an essential part of creating artwork for print. Professional designers will always extend (or 'bleed') background elements and images beyond the edges of the document by an additional 3mm or so. This prevents unwanted white borders around the edges of a printed document.

Commercial printing presses are no different to your desktop inkjet or laser printer - they cannot print to the very edge of a sheet of paper. To get around the problem, we print your design onto a larger sheet of paper and then cut it down to size. Most conventional and digital printing presses suffer from slight sheet-to-sheet misregistration. In other words, due to slight movement as the paper passes through a press, your design may not be printed in exactly the same position on every sheet of paper. We're not talking about much - usually only fractions of a millimetre. Also, when the guillotine operator is trimming your design down to size, it is not possible to cut exactly along the edge of your design.
To get around this problem, designers use bleed. This simply means that they extend beyond the edge of the document (by between 3mm and 5mm) any elements which should touch the edge of the paper. As a result, any inaccuracies which occur during the printing or finishing process shouldn't cause any problems.

What is comes down to is making your artwork slightly larger than necessary so that it can have an extra 3mm all the way around and making sure there is nothing that needs to be printed in this area (e.g. text), but that it will still look acceptable if it is printed (i.e. it is a continuation of the background colour/image).
 

Additional Resources
Bleed: A detailed guide (incl instructions for Photoshop and Indesign)
Wikipedia: Bleed