Landau is a term used in the automotive field to denote a particular style of roof or top. Unfortunately, what exactly is meant by the term is inconsistent.
In early days, before World War II, the term generally meant a car where the front row of seats had no roof or a convertible cloth roof that could be folded down, but the second and subsequent rows of seats had a full hardtop roof. This was generally an option for expensive cars, where the driver would not be the owner but rather a paid chauffeur; he was left to deal with the elements, while the passengers got protected, in a manner similar to a horse-drawn carriage.
Since then, the term generally is used to refer to a car that is made to look like a convertible but really isn't, generally by means of a vinyl roof which may be padded under the vinyl to make it more convincing. Often, but not always, the illusion is cemented by the fitting of simulated S bars to the sides of the wide rear pillar, mimicking the outside bars on a traditional convertible's roof that on a real convertible are part of the load-bearing structure of the folding frame holding up the roof.
Landau roofs were quite popular in the late 1960s through the 1970s, particularly on American luxury cars (or wannabe luxury cars). Cadillac produced models with landau roofs until very recently.
Most American hearses are landaus, and you'll probably be familiar with the landau style by thinking of the way hearses are styled, with a vinyl roof, very large rear pillar area and chromed S-bars on the sides.