cropmarks1 cropmarks2
This shows the crop marks before trimming This is after trimming

Printers use cropmarks (short black lines) to indicate where the printed sheet is to be trimmed.  These marks are placed outside of the trim area, and will be cut off when the printed piece is trimmed to its finished size. 

In the above example the edges of the paper are represented by blue lines.
artwork1 art2
This artwork does not have a bleed. This artwork has a bleed.

A bleed refers to printing that goes beyond the edge of the sheet after trimming.  The printed sheet is trimmed after printing to ensure the ink runs fully to the edge and does not stop short of it (leaving a white line). 

A bleed is generally 1/8" from where the cut is to be made.
textsafe1 textsafe2
This artwork does not have a text safe margin. This artwork has a text-safe margin.
 
A text safe margin of a minimum 1/8" is necessary to be sure your text (or graphics) are not cut off unintentionally.

While we keep our tolerances as tight as possible, during the separate printing and cutting processes, shift of up to 1/8" are possible.

We typically recommend a 1/4" text safe margin to ensure the best results.  Business cards in particular must have the minimum 1/8" text safe margin.