I should let CMKeller or Zev comment on the Orthodox approach, but I’ll try to be even handed [/grin]
The Torah is very ambiguous about what constitutes “work” on Sabbath; wood-gathering is clearly not allowed, and food gathering seems to be in the same category. The later rabbis argue that there are 39 (? if I remember aright) categories of “work”, based largely on what was done in constructing the Temple: carving, hewing, gathering, starting fire, sewing, etc.
Over the centuries, new activities are interpreted (acceptable or prohibited) based on the ancient rules. Hence, electricity was deemed to be “fire.” The rules regarding fire are that you cannot make a fire on the Sabbath, nor extinguish one, but that you can use a fire that is already going. Before electricity, observant Jews would keep the fire going and put a pot of stew on it befor Sabbath, and then let it cook all during the day, to eat later in the afternoon. With the advent of electricity, the same approach is taken: the stove is turned on before Sabbath and left on, if you want hot food.
Lights on a timer are deemed to be OK, if the timer was set before Sabbath. The rules are intricate and complicated, and very detailed.
Philosophically, the idea is not to interfere with Nature on the Sabbath. Not to build, not to make, not to create, not to fight against Nature.
However, an exception is always made for anything life-threatening. Seeking medical treatment is never a violation of Sabbath (well, OK, I guess something elective like cosmetic surgery, that wouldn’t do, but you know what I mean). There are commandments which one is supposed to accept martyrdom rather than violate, but the Sabbath is not one of them.