There is likely more than one correct answer to this, but here are a few answers that vary and may be true in multiple environments.
Student athletes
If we are talking about athletic students who are going to be "student athletes" (i.e. play on the universities intercolligiate sports teams) then the incentive is to win those tournaments. Depending on sport, winning an NCAA tournaments can be a very valuable endeavor. Additionally, as noted in the answers to this question, noted in the comments above there is a publicity value to having a notable sports team.
Athletic Non-Student Athletes
- Involvement in extra-curriculars with attendant good grades shows that students aren't just getting by in high school, or dedicating all of their time towards studying, and therefore are more likely to succeed. In these cases, members of the student body, people in the band and on the yearbook committee get more or less the same boost.
- A different type of student participates in sports, and by seeking out those students, you can improve the chances of a well rounded student body. People who are sports minded are often different kinds of competetive from your "type A" valedictorian-type students, where team values are rewarded. Also, Charles Murray has noted that sports participation is more highly correlated with lower SES, although not perfectly. Relatedly, there are many who grow up in a very poor environment, who pursue sports because they feel, wrongly, that it is their only ticket out. They have shown significant capacity to learn, but not enough capacity to play on the college team, and seeking those students provides them an opportunity the otherwise might not have.
- For some universities athletecism is part of their mission. For example the U.S. military academies require participation in intra-mural sports for all students, for somewhat obvious reasons. One can imagine that other schools might have primary training objectives that require physical fitness.
- Some schools make an athletic student body a part of their sales "pitch." Places the University of Colorado play up the active nature of the campus and the student body, and consequently they want to ensure at least a modicum of that. On the other hand, if a student body is organically athletic, then recruiting students who are interested in that sort of activity is part of the "goodness of fit" that selection entails, and schools want to ensure that their offers are accepted, so they will tend to opt towards students that are like their current students, to increase the probability that the students they admit come.
- Finally, the advantages of fitness for intellectual activity are well documented. Admissions may simply be trying to do what they can to skew in favor of this additional criterion for admissions that increases the probability of success at school. It is probably a less reliable proxy variable, but since all schools are chasing pretty much the same graduates they could be using a "Moneyball-esque" strategy.
All of this is based primarily on my own experience and conjecture. I doubt highly that any of these factors weigh heavily at any school, and certainly not all of them at any school. I doubt, further, that many schools actively recruit athletic students on principle, any more than they recruit people from a language club or the choir, but these are at least some reasons they might want to.
