Vinyl roof refers to a vinyl

Vinyl

A vinyl compound is any organic compound that contains a vinyl group ,which are derivatives of ethene, CH2=CH2, with one hydrogen atom replaced with some other group...

 covering for an automobile's top. This covering was originally designed to give the appearance of a convertible to models with a fixed roof, but eventually it evolved into a styling statement in its own right. Vinyl roofs were most popular in the American market, and they are considered one of the period hallmarks of 1970s Detroit

Detroit, Michigan

Detroit is the major city among the primary cultural, financial, and transportation centers in the Metro Detroit area, a region of 5.2 million people. As the seat of Wayne County, the city of Detroit is the largest city in the U.S. state of Michigan and serves as a major port on the Detroit River...

 cars. Vinyl roofs were also very popular on European- (especially UK-) and Japanese-built cars during the 1970s, and tended to be applied to sporting or luxury trim versions of standard saloon (sedan) models

The first use of this technique goes back to the 1920s, when leather, canvas and vinyl were sometimes used along with landau bars, to give a fairly accurate reproduction of a horse-drawn carriage's movable top.