One type is the touch-screen, where you only press the buttons or depress certain places on the screen to indicate your vote. These machines became notorious for their suspicious results (as in the GA 2002 election where the votes were counted completely in cyber space, no paper at all). The touch-screen machines can be and now usually are outfitted with a device like the print-out at a grocery store after you buy you groceries, except that the voter can't take it with him or her. The print-out can be checked by the voter as it prints out but it remains with the machine and is supposedly retained in case of a need for a recount or audit. This is what Beth Clarkson wants to look at, the print-out that supposedly tells the tale of each particular vote. The voter's name is not on the print-out. Kobach won't let her look at these print-outs.
Another type, the preferable type, the opti-scan, uses paper. The voter votes entirely on paper. The machine is used only to count the votes by running the paper ballots through the machine. I suppose the vote is numbered so it can be matched with the voting rolls but Clarkson would only look at the paper ballots. She would not be matching the number on the ballot with the list of voters. Clarkson is only trying to make sure that the machine has not been illegally or maliciously programmed so as to rig the vote, and the only way to check this is ON PAPER.
Kansas uses both these types of machines, and both types can be maliciously programmed when those in charge are screwballs and cheats.