What is the meaning / definition of Galileo in the hospitality industry?

Galileo is a Global Distribution System (GDS).
It refers to the reservation tool which travel agents use when making an air, hotel, car or other travel service booking.

GDS serves not only travel agents but also many different companies including airlines, ground handlers, hotels, railways, car rental companies, airports, cruise lines and ferry operators.

The Galileo system is managed by Galileo International (owned by Travelport). It is serving users in Europe, South America, Asia and Africa. 
In the United States, Canada, Mexico and Japan it is operating under the name Apollo.

See also:

Synonyms