When we print your business cards, leaflets, posters, stickers etc we don't print directly onto the final sized sheet, such as A5 for a flyer. We print them on larger sheets as our printing machines can't print to the edge (just as your desktop printers can't) and also we can get lots on one sheet which can be more efficient.
Due to the printing process, as accurate as they are getting now, there is still a slight movement between sheets and so between one sheet and the next there could be a slight difference of position. So without a bleed area these slight movements would become apparent when trimmed, as a white edge may appear.