Staging is a working copy of a website or application where changes are tested before going live – identical to production but invisible to customers and search engines.
A professional deployment process uses at least three environments: local (the developer's machine), staging (testing and client approval) and production (what users see). A change travels along this path and reaches "live" only after approval.
Why does the client care? Because staging lets you safely view and click through a new feature, give feedback and approve – with no risk that customers see half-finished work or that an update takes down a working store.
A vendor quality signal: the question "where will I be able to test changes?" should have an instant answer. "We'll fix it directly on the live site" is an invitation to disaster.