A company is said to be “listed”, “quoted” or “have a listing” if its shares can be traded on a stock exchange.
To be more accurate, it is the securities that are listed, not the company. The phrase “listed company” is widely used to mean a company that has listed ordinary shares.
It is possible (although not common) for a company to have listed debt securities but not listed shares.
In the UK inclusion, on the Official List is a pre-requisite for trading on an exchange. It is inclusion on the official list that defines a listed company.
The Official List is published by the UK Listing Authority.