A week is the guild’s cycle of assignments and pay. Finish an expedition or advance the week at base, and the mercenaries who stayed behind train or rest according to their assignments.
Open "Climb This Week" from "Base" to prepare an expedition. For a week at home, review assignments and press "Next Week", checking the wages shown on the button.
Spend a week on recovery if your main party has injuries or fatigue. Training adds fatigue, so assign rest to the people you need for the next expedition.