Research Experience for Undergraduates, or REUs as they are more commonly known, are programs run by mathematics departments or institutes and provide undergraduates the opportunity to actively participate in mathematical research projects. Most REUs have a specific focus such as the University of Connecticut's REU in Fractals and Financial Math or Texas State's REU in Algebra, Combinatorics, and Statistics. REUs are about more than just completing a specific research agenda, they are also meant as a way to introduce undergraduate students to the tools and techniques of mathematical research more broadly and to start to integrate students into the mathematical world through cross-institution friendships, mentoring, and conference presentation opportunities.
If an REU sounds interesting to you, but you want to learn more Deanna Haunsperger and Steve Kennedy wrote an article for the Mathematical Association of America a while back where they interviewed REU participants call, Is an REU for You?, which can help you get a better sense of what the day to day of an REU is like.