Mystery shopper is a person who is employed, often by the owners, to visit shops, hotels, etc, incognito, and assess the quality of the service offered. The mystery shopper poses as a normal customer and is given a specific task, such as purchasing a particular product or asking certain questions. Mystery shoppers may check on any aspect of the customer experience, from sales presentations to how well displays are maintained to in-home service calls. A mystery shopper is someone hired to pose as a customer and report on the quality of service received and how well a store or chain of stores is being run. (Collins English Dictionary)
In Sigma Research, one of the data collection techniques of quantitative methods for the evaluation of service performance such as banking, is usually done by sending a researcher who acts as a customer (mysterious shopper). The researcher will fill in the observation sheets which are analyzed later.