The term 24 hour call centre simply refers to a call centre which is open 24 hours and usually 365 days a year (although not always). They are normally for customer service or technical support inbound calls where calls come in throughout the day and night. Many outsourced call centres who operates a per minute billing operation offer this service. Some outbound call centres are open 24 hours a day 5 or 6 days a week when they service multiple regions. For example, there are some call centres in India & The Philippines who service outbound calls for Australia, The UK and The United States and have agents working 24 hours a day.
Operating a 24 hour call centre can be a tricky process due to staffing, increased pay and low efficiency of the operation due to low call volumes. These are some of the reasons why so many "out of hours calls" are handled by call centre companies. They are often operated on a cost per call or cost per minute basis as opposed to a dedicated agent pay per hour model.