A sourdough starter is a live culture of wild yeasts and lactic acid bacteria kept in a mixture of flour and water. The yeasts produce the carbon dioxide that raises the dough; the bacteria produce the acids that give the bread its flavour and its keeping quality.
It is maintained by discarding part of the culture and feeding the rest with fresh flour and water — refreshing, in baking terms. The proportions and the interval vary by recipe and by the temperature of the room, which is why two bakers with the same starter get different results.
Why recipes disagree about it
A starter's behaviour depends on hydration, flour type, ambient temperature and how recently it was fed. Books therefore describe schedules rather than fixed times: "until doubled" is a state, not a duration. A recipe that gives only clock times is assuming a kitchen it cannot see.
Starter, levain, preferment
The words overlap and are not interchangeable. A starter is the culture kept alive between bakes. A levain is a portion of it built up specifically for one dough. Preferment is the general term covering both, plus yeasted versions such as poolish and biga that use commercial yeast rather than a wild culture.