To save is to keep safe. So, you might save money for college, save a kitten from drowning, or save a dropped football.
You can save a choking person by giving them the Heimlich maneuver, or save a stray puppy from running into the street. There are other ways to save things, too, like when you keep them for later: "You can eat your brownie, but I'll save mine until after dinner." Or when you spend less money: "I'll save by buying this at the used book store." The Latin root is salvus, "safe."