A company or government agency that provides

• carriage of people and/or goods over long distances, such as an airline, railway, moving company, busline or freight hauler
• carriage of telephone or message services from one place to another.

What makes a common carrier significant is that, in exchange for limited liability (generally, they're not responsible for whatever they're carrying), the organization gives up some control over who they accept as customers, and they are subject to increased government regulation. Essentially, they are partially assimilated into the government.