In offset lithography a printing plate, which is most often made from aluminum, contains an image of the content that needs to be printed. When the plate is inked, only this image part holds ink. That inked image is subsequently transferred (or offset) from the plate to a rubber blanket and then to the printing surface. The process can be used to print on paper, cardboard, plastic or other materials, but these have to have a flat surface.
Below is a picture of a 4 color sheetfed printing press. At the far end is the intake where individual sheets of paper are automatically fed into the press. The 4 towers or printing units each print one color, typically black get printed first, followed by cyan, magenta and yellow. The stack of printed sheets is visible on the front of the machine, underneath the press console & monitor which the press operator uses to control the press.
For higher volume work offset presses use rolls of paper. The picture below shows such a much larger web press. It is so fast that the printed paper needs to be force dried. The black unit at the end of the press is an oven.
Offset is nowadays the most widely used printing technique for an extensive range of products such as books, newspapers, stationery, corrugated board, posters, etc.
There is a trend that printing promotional material is gradually migrating to digital printing while some packaging printing is moving to flexo.
You can find more information on the page dedicated to offset printing.