ACM ICPC is basically the Olympics of Competitive Programming.
The significance can vary from person to person but sometimes Universities and Companies look favourably at good results in such competitions.
To prepare for it they generally practice either on UVA online judge (1800 problems) or Topcoder.
To see how insanely challenging it is, try to solve even 90 problems out of the first 100:
https://uva.onlinejudge.org/index.php?option=com_onlinejudge...
It looks good on the resume, especially if the person reading the resume has been to that kind of competitions too.
When I was at nearby USF, our programming contest teams were student-run. It's not a priority for the department and there is a lot of inconsistency as students come and go. There's also a smaller pool of participants to draw from. We did reasonably well for a little while when I was there and put a bunch of time into it, recruiting, teaching, running practices with and without other unis. But it takes a lot of effort.
However, Caltech itself doesn't care that much about its team's performance.