The Panama Canal is a canal designed by President Theodore Roosevelt to move people and goods faster. It was a popular traveling route during the famous Gold Rush era. However, there were a plethora of issues during the process of building it, including diseases such as malaria.
The Princess Andromeda's crew use it to get to San Francisco as the canal is the fastest way for a ship to travel between coasts. They use the canal, so that Luke's forces could meet at Mount Othrys near San Francisco.