A java jacket is a slip of cardboard that fits around a paper coffee cup, so that a person can hold the hot cup without burning their fingers.
This became popular in cafes sometime in the 1990's, when cafe owners realized that people were taking two cups -- one for the coffee, and one to insulate the first cup.
Presumably the brown recycled-paper java jackets are cheaper than the extra cup.
The java jacket was patented in the U.S. in 1993 by Jay Sorenson. He tried to sell the coffee cup sleeves to Starbucks, but Starbucks took his idea and developed a similar product. Despite this treachery, Sorenson's company sells about 10 million java jackets a month.