A time clock (now electronic, of course) used to be a machine that looked like this: http://tinyurl.com/obkmazx A worker would insert a card into the machine, and it would print the time on the card. Like a number of machines of that kind, it cut a physical notch on the edge of the card to "remember" the position of the last entry so that each time would print one line below the last one. It thus kept a record of when you arrived and left work. To clock in or clock out means to put your card in the machine and record your time of arrival or departure.

Clock in = start work Clock out = finish work "I have to clock in/out" means that they physically have to clock in. With a card or a code or something. "I'm at work till six" means "I will be working/at work until six o'clock" "My work is ten to six" means you work from 10:00 to 18:00 or 22:00 to 06:00.

Clock in and and Clock out and phrases like, "I'm off the clock" and "I'm on the clock" related to working. Being on the clock, means that you're currently being paid to do your job. And being off the clock, means that you're no longer being paid to do your job. So lets say you're trying to leave to day, and your boss or customer ask you to do something that relates to your job, but you're going home for the day, "Sorry buddy, but I'm off the clock." Means something very similar to, "I'm not working right now." or "I won't be working right now." Clocking in and out, also relates to working. Clocking in, means that you're getting started with your working day, and or you're getting your hours that you are working registered with the company so they can fairly compensate you for your work. Clocking out, means roughly the opposite. It means that you're getting ready to leave from your work, and or are registering with company that you are no longer working.