A worldship is a rocky body sealed off, terraformed, equipped with slower than light and FTL drives and then sent into the galaxy.
Developed in the 25th century by AfrikaCorp the concept is relatively simple: a rocky terrestrial (and in rare cases jovian) world is found in a random system. They can be as small as Ceres (and most are) or as big as Earth, but the latter are rarer due to costs and time.
The mass of the world is then adjusted to make human life on the surface easier to live on. Some worlds are not touched in that sense, like Ceres was.
When that is done, the world is encased in a clear but strong and sturdy clear sphere that also doubles as a fake sky when in deep space and is also the source of sunlight and warmth when the planet is in deep space.
After the dome is in place, an atmosphere is added and anything else that may be necessary. After that, plants and animals are incorporated until it is a temperate Class-E world built to specifications.
The planet is then outfitted with enormous STL and FTL engines and communication systems as well as a massive and advanced AI to keep track of the planet’s ecology and take care of the population.
The colonists are then brought in through one of the massive towers that hold up the sphere above the planet. The computer has two basic travel settings. It can either be programmed with a specific route or it can be programmed to head in a random pattern around the galaxy. The civilizations who decide to stay low tech choose the latter while others choose the former, enjoying alien skies without leaving their backyards.
While certainly not the first one built, the most noted worldship is Ceres due to its more exotic culture and plant and animal life and it as well as its amazing longevity.