Sabbath mode serves two functions.
One is that it overrides the automatic shutoff - these days, ovens shut off if you leave them on for over 12 hours. This makes perfect sense - this way, if you forget to shut it off, you waste less energy and it's safer. However, many people use their ovens to cook food over night, and others use it to warm dry food for lunch or even a dinner. This requires the oven to be on the entire time.
The other is more a problem for Jewish holidays - on holidays, it is permitted to raise and lower temperatures. This absolutely means one needs the shut-off override - holidays being 48 hours - but there's another issue. The oven temperature controls are now electronic, with an LED display. Changing the temperature is therefore doubly problematic on Yom Tov.
Sabbath mode turns off the display, but allows temperature change by pressing the appropriate button - each press raises or lowers the temp by 25degF. It solves the electronic problem by putting in a delay - the temperature only changes after some random time between 30 to 90 seconds, so I'm not directly changing the temperature. This works because we're really not sure electronics are forbidden anyway.
