Contests were first released sometime in mid-2005. They are competitions that users enter to compete for prizes. The original contests began in mid 2005 (as seen on the Wayback machine) and do not happen very much at all now. The original contests would be put on Roblox's Blog pages. The host was one of the people from the staff. Their prizes were also hard to get such as video contests.
The first contest started on June 17, 2005, it was named "Fend off the bots!", in which you have to build something to stop robots from catching you.
More contests continued on over the months, such as Steer the Spheres (#1 and #2) and Balance. 2010-2011 was when contests were really popular, with over 50 of them during that time period.
Contests were sometimes criticized when users won a contest with a place that had little-to-nothing to do with the overall theme.
On the prizes page, it shows the prizes. It will have prizes for Highest Rated Places, and sometimes prizes for Most Accurate Voters.