Short for magnetic swipe (ID system).
Mag-swipe cards are typically credit card sized, with a black strip of magnetic material like on the back of a credit card, in fact a credit card is a mag-swipe card. Corporate ID cards usually have a mag-stripe too, for unlocking doors, or access to elevators, things like that.
The mag-swipe box itself is usually a few centimetres longer than the card, with a slot that goes the whole length of the box. The slot is built with a funnel shape at one end so a person can easily get the card in position. The card is pulled the length of the slot, with the stripe inside the slot, and a reader picks up the information from the card in a method similar to the read head on a walkman.
There are variations on the mag-swipe design, sometimes the slot is vertical and sometimes horizontal, sometimes the slot doesn't go all the length of the box so there's a particular way you have to place the card before you swipe, but generally they all have pictures and/or arrows that make it easy to figure out which way it goes.