What is a funicular railway?

In the news about the recent accident at a ski resort in Austria, the reporters called the cable car that carried the skiers up the mountain a "funicular railway." What is that and how does it work?

1965: The Inauguration of a Funicular Railway in Greece's Capital

Incline Railroad or Funicular Railroad

Tanfield Railway Blog: Funicular Railways

Fribourg's Sewage-Powered Funicular Has Been Running Since 1899

Look out below! Europe's steepest funicular railway has a gradient

Fløibanen funicular - visitBergen.com

Skarloey Resort Funicular Railway's own David and Gabriel : r

Water Powered Funiculars

140 evacuated from mountain restaurant after funicular malfunction