The space shuttle was a large missile-shaped spacecraft owned by the Precursors. At the end of Jak 3 they invited Jak with them, into a journey to space and more planets. Jak agreed, but mysteriously appeared later behind Daxter though no one saw him exit the shuttle.
It's believed there were more Precursors inside the shuttle, as when Jak enters it, a short "our hero!" can be heard once the screen is filled with a blinding light.