Zeki is the western naming convention for the ship that combines Zero Kiryu and Yuki Kuran. The name combines the Zero and Yuki to create the name Zeki and has no meaning beyond that. It's also meant to be the love between Zero and Yuki.
Zeki was voted most popular ship in the January 2008 Lala poll with 1700 votes. It is also the most popular ship in the storyline.