To ensure that no unprinted edges will occur, an image or color will be printed beyond the edge of where the sheet will be trimmed. The surplus that needs to be trimmed off is referred to as the "bleed". This means that whatever artwork one wants to print on a surface should be made a little bigger than the surface itself, so that when said surface is trimmed, it is colored in its entirety.
In the image below, you can see how there is a white line on the left side of the box. This is one of the reasons why having bleeds is useful in packaging.
As a rule of thumb, it is best to have your artwork 'bleed' over to the other side of where a fold occurs. You can see in the examples below that the artwork goes onto the other side of the packaging.
An alternate solution in this case is to have the box be covered in the same color where folds occur so that you won't have the issue.