What is the ceiling in the weather network?

Simple answer: where the lowest layer of clouds begin.

As @Darth_Algar said. It is used be airmen to determine how high they can fly onvisual flight rules.

You live in an area where the clouds are aloft because of the Rockies. Where I live, the ceiling is often well below 5,000 feet, sometimes as low as 100 feet, because of the marine layer, the fog off the ocean. A storm front moved in yesterday, and it has been overcast here all day, with the ceiling at around 2,500 feet. With ten to fifteen miles visibility, I could see the base of Mt Diablo, but not the top.