Seedships are the spacecrafts that ferried colonists from Old Earth to their new worlds, primarily during the Hegira. They used Hawking Drive technology to engage on long voyages while their passengers were in deep sleep. Ousters, Templars, and all other human groups leaving Old Earth used seedships. Besides their human cargo, the seedships had defense mechanisms, and were loaded with provisions for the initial colonization process. They also presumably carried Terraforming instruments.
On the many different worlds of the Hyperion universe, human populations that had gone native - the Indigenies - had usually arrived via seedship. For example, the Bikura are said to have arrived in seedships. Sad King Billy used five seedships to move his court from Asquith to Hyperion. Huge seedshipsp colonized Barnard's World, only the second extrasolar world to be conquered. Siri's ancestors arrived via seedship to Maui-Covenant. Tibetan/Chinese Old Earth seedships colonized the world of T'ien Shan.
Seedships also carried farcaster capabilities during the Hegira, thus spinning the web of what would become the Hegemony.