(covers information from several alternate timelines)
Kes' starship was a small vessel of unknown origin used by Kes.
In 2376, Kes crashed her vessel into the hull of the USS Voyager, so she could board it and use Voyager's warp core to travel back in time to 2371. In this timeline she succeeded and her ship was destroyed.
In the past she was defeated, with her actions changing the future, creating a new timeline in which her past self took precautions to prevent history from repeating itself. After viewing a hologram of herself recorded in 2371 asking her to stop her malevolent ways, the 2376 Kes ceased her actions. Afterward, she decided not to stay on Voyager and went back on her ship, and used it to return to her homeworld, Ocampa. (VOY: "Fury")