The term bleed is used for all objects overlapping the border of your document. If any element on your document layout makes contact with the document border you will have to use bleed. The trick is to place the element so that it goes over the border where the document will be cropped after printing. This means that when the document has finished printing and is ready to be trimmed it will be printed right to the edge of the document without a white unprinted border.
For example if you're working on a brochure with images against the sides of your pages. You'll supply us with a document somewhat larger than the final document will be (3mm bigger on every edge preferably).
After the brochure is printed it will be cropped to its correct size. The bleed in your document gives the cropping some room for error. The paper itself can expand or contract, the cropping machine could be setup wrong or the person working on the brochure could make a mistake. There are a lot of factors that could go wrong with the cropping, if you weren't using bleed the images wouldn't be neatly aligned with the side of your printed document.
Two kinds of bleed
Bleed can be a full bleed or partial bleed. With a full bleed you have objects running off your document on all sides. With a partial bleed you'll have a couple of elements running off the document.
Critical content refers to any element of your document that you definitely don't want to be trimmed off. To avoid this from happening our designers never put critical content any closer to an edge than 5mm and we suggest you do the same. This means that when your 3mm (at least) of bleed is trimmed off you should still have a 5mm (at least) margin between the edge of the card and the start of any critical content.