A slitter is a piece of equipment
(sometimes called a "business card slitter" or "card slitter") with a set of rotary blades and matching rollers, sheet feeder and output tray such that sheets (or "strip
s") of paper run through it will get parallel
This is the most common way to produce business cards. Either 3.5 inch wide strips are run through the slitter with blades 2 inches apart to produce cards, or full sheets of paper are run through one way and then the resulting strips run through a second time (with the slitter adjusted)
When starting with a whole sheet, there are two common ways to get cards. 8.5 inch by 11 inch sheets are the commonly used size in the United States. One is called "12 up" and starts with the blades 3.5 inches apart to produce three 8.5 inch long strips which are then cut a second time with the blades 2 inches apart to produce the final cards. The other is "10-up" and has 2 strips of 10 cards each cut (which involves fairly wide margins)
If you've been paying attention, you'll notice that 3.5 * 3 == 10.5 and 2 * 4 = 8, while the sheet of paper is probably 11 by 8.5 -- the extra half inch is either spread out through the cards (giving you the unprofessional looking 3 2/3 inch * 2 1/8 inch cards), trimmed off the outside edges and discarded or (with the better quality slitters) removed from the outside edges *and* in small "gutters" between cards, allowing for the printing to have a layout with colors that run up to edge of the card without having to worry about getting color from another card or little bits of white where they shouldn't be.
In the United States, Thermotype is the best known producer of the higher-end slitter models. (With plenty of competition in the lower end models)
Better models can also perforate and score.