ACM International Collegiate Programming Contest (ICPC) is one of the largest and most prestigious collegiate programming contests in the world. Students compete in teams of 3 to solve a series of problems of a mathematical/algorithmic nature. ACM/ICPC is a multitier competition. Universities compete in regional contests. Then winners of regional contests advance to the world finals. From each region, at least one team goes to the world finals.
Columbia University falls into the Greater New York region. Although the smallest region in North America, it is highly competitive. Each year, more than 50 teams attend the Greater New York regional contest, including teams from Columbia, Princeton, Cornell, and Yale.
There are a number of benefits of competing, or even just attending practices. You get to learn a lot about problem solving and algorithms; you get exposure to the type of problems that interviewers (for tech/finance/etc companies) love; it is a valuable addition to a resume; you could win great prizes, get all-expenses paid travel if you advance past regional contests. The world finals have been held in Hawaii, Prague, Stockholm, Tokyo, and Harbin. And of course, there is always the fun of problem solving and meeting new people!