A fabless semiconductor company is one that designs and markets semiconductors, but does not manufacture them.
This has become a common business model because setting up a fab (a semiconductor factory) is enormously expensive, and has become more so as the technology has become more complex. Apart from the sheer cost, there are other barriers to entry such as the patents held by the major semiconductor companies.
This means that, for many companies, manufacturing themselves requires too big an investment to be justifiable. These companies contract out their manufacturing and concentrate on other aspects of their business.
The major semiconductor companies (Intel, IBM, etc.) have their own fabs. Some of these do contract work for fabless manufacturers. There are also companies that are specialist manufacturers, that do not design or market their own products (such as TSMC). These tend to be well known within the industry but not outside it.