Flour: The cornerstone of sourdough, flour provides the food yeast feeds on, and hosts flavor-producing friendly bacteria as well. Combined with water, flour's protein develops into an elastic web (gluten) that traps the carbon dioxide gas given off by yeast, making dough rise.
Water: Water activates the gluten in flour. It's also a vital necessity for growing yeast; and is the "solvent" that disperses all of the remaining ingredients.
Yeast: The wild yeast in sourdough, Saccharomyces exiguus, is a different strain than domestic (manufactured) yeast (Saccharomyces cerevisiae). However, once wild yeast establishes a base population, it grows just as readily as packaged yeast. Yeast's main job in sourdough is to produce carbon dioxide gas, which makes starter or dough rise; and alcohol, which gives bread flavor.
Salt: Not only does salt add flavor to bread, it controls the rate of fermentation by slowing down how quickly yeast consumes sugar. This ensures that there'll still be food left for the yeast when the risen loaf goes into the oven — enough to produce one final large discharge of carbon dioxide, resulting in oven spring. It also leaves enough sugar for optimum browning of the loaf's crust during baking.
Sugar: Carbohydrates in flour are broken down into complex sugars by an enzyme, amylase. Those complex sugars are broken down still further by friendly bacteria, creating the simple sugar yeast loves to eat. This is an efficient process; thus there's no need to add any sweetener (granulated sugar, honey) to your dough to "get the yeast going" or feed it.
Fat: Oil or butter will yield a softer crumb in bread, plus create rich mouthfeel. Beyond that, fat isn't a necessary component of sourdough bread.