Jewish law prohibits Jewish people from doing any form of melachah (The Hebrew word for "work") on Shabbat. The Talmud defines Melacha as one of 39 categories of activity that Jews are prohibited from engaging in 39 Melachot (activities) on Shabbat.
The 39 Melachot are not so much activities as categories of activity. For example, while "winnowing" usually refers exclusively to the separation of chaff from grain, it refers in the Talmudic sense to any separation of intermixed materials which renders edible that which was inedible. Thus, filtering undrinkable water to make it drinkable falls under this category, as does picking small bones from fish. (Gefilte fish is a traditional Ashkenazi solution to this problem.)
In the event that a human life is in danger, a Jew is not only allowed, but required, to violate any Shabbat law which stands in the way of saving that life.
The 39 Melachot are (Mishna Shabbat 7:2):