From the FAQ:
About challenges
What is a challenge?
A government challenge or contest is exactly what the name suggests: it is a challenge by the government to a third party or parties to identify a solution to a particular problem or reward contestants for accomplishing a particular goal. Prizes (monetary or non–monetary) often accompany challenges and contests.
Challenges can range from fairly simple (idea suggestions, creation of logos, videos, digital games and mobile applications) to proofs of concept, designs, or finished products that solve the grand challenges of the 21st century. Find current federal challenges on Challenge.gov.
About Challenge.gov
Why would the government run a challenge?
Federal agencies can use challenges and prizes to find innovative or cost–effective submissions or improvements to ideas, products and processes. Government can identify the goal without first choosing the approach or team most likely to succeed, and pay only for performance if a winning submission is submitted. Challenges and prizes can tap into innovations from unexpected people and places.
Hard to think of better PR for topic maps than being the solution to one or more of these challenges.
If you know of challenges in other countries or by other organizations, please post or email pointers to them.