The term government funded research is used to describe scientific studies which are paid for by the government. During the Second World War, the governments of each side invested heavily in scientific research in order to try and develop technologies which would give them an advantage in the war. Technologies such as radar, rockets, jet engines and, of course, atomic weapons emerged as a result.
After the war, the practice of governments funding scientific research remained in place. Some of this research was military in nature. However, even research with no obvious military application is funded too. Governments recognize that there is a public benefit from technological advance and that private corporations can only be expected to push technological advance within a narrow sphere, one that is likely to lead to profitable applications in the short to medium term. As a result, governments have shown a willingness to provide funding for other scientific research conducted, primarily, at universities.
Typically, scientists who wish to receive government funding for their research will draw up a proposal, setting out the goals and methods to be used, together with a budget which they will ask the government to provide. In some cases, government may also employ scientists directly and provide funding for the work they do while controlling it completely.