In a bread formula, levain usually means a portion of sourdough starter refreshed with flour and water for use in a particular dough. The baker can adjust its flour, hydration and ripeness separately from the starter kept for future baking.
Levain also appears in the French name pain au levain. It is not necessarily a stiff mixture: both liquid and firm levains are used. Include its flour and water when calculating the dough's baker's percentages.
Reference: Further reading.