REU stands for Research Experiences for Undergraduates. It is a type of program put together and funded by the National Science Foundation (NSF). National laboratories and observatories also have programs
The REU program and other summer research programs are an opportunity for undergraduates - particularly those majoring in Physics &/or Astronomy - to get paid to work on a research project for the summer with a scientist. Typically, these REU programs are hosted by a University or a National Laboratory or Observatory. The NSF provides money to the site so that they can hire 6-10 students to work with faculty who are interested in hosting a student. Typically all the students are from different universities and colleges - a chance to meet other people!
Usually the only requirements to be eligible for one of these programs is that you are pursuing an undergraduate degree in physics and/or astronomy. The REU specific sites are usually only open to students who are currently STILL pursuing their degree (i.e., NOT graduated seniors), however more and more sites are also opening up to graduated seniors and first year graduate students. For example, NRAO and most NASA centers encourage graduated seniors and first year graduate students to spend the summer doing research at one of their sites. Don't write off a summer research job just because you are graduating - spending the summer before graduate school at one of these sites can be an important foot in the door to a future research project.
There are a number of reasons to undertake research projects in the summer: (1) Opportunities to get involved with types of research you may not have here at University of Iowa; (2) a chance to see how a national laboratory or observatory runs; (3) To make contacts at other universities, laboratories, observatories (these may come in handy later if you go on to graduate school); (4) to see what physicists and astronomers REALLY do; (5) to spend a summer somewhere really interesting (Southwestern US, Puerto Rico, California, ...).
The dates of employment absolutely depend on the program. Some programs have set dates, some do not. There is usually quite a bit of flexibility to accommodate for some summer vacation time as well as different schools finishing at different times in May and June. Usually the dates of the REU programs are early June - mid August.
Typically, the summer stipends are very reasonable (glancing over the Summer 2008 REU program stipends, it looks like on average ~ $500+/week or more - quite generous! - or a fixed stipend for the entire summer) with money also supplied for housing and usually the travel to/from the REU site is covered. The NSF likes to support students to travel also to the national astronomy or physics meetings and present a poster on their summer research!
Often the housing is set up by the REU site - in dormitories or houses the site maintains. Other times, the REU students get in touch via email before the program starts and agree to rent a house together and to cook meals. There are usually a lot of weekend outings to explore the local environment.
I have given a fairly complete (but by no means) exhaustive list of REU sites and other summer research opportunities at major labs and national observatories on this website. However, more options exist (especially in some specialized physics areas that I haven't covered) so it is worth poking around the internet for other opportunities. See this page for tips on how to apply. Typically the applications for REU positions are due between early January and early March, and you will be offered positions between March and April.
If you are a first-year student, it may make the most sense to get your feet wet with research with one of the faculty in the Physics & Astronomy department here. Some of these 'on site' research positions often give preference to students who are sophomores or juniors and who have shown initiative by getting inovlved with research during their first or second summer. Or there may be other constraints that require you stick around campus for the summer - in any case, many physics and astronomy faculty have money to support students for the summer (full time, part time, or for part of the summer). It is best to approach faculty early in the spring semester and find out what options exist for research positions. Professor Van Allen has started a fellowship for student summer research and the university also has some funds through the Honors Program for undergraduate research - both of these require hooking up with a faculty member and outlining a proposal together. A good time to talk with professors is in the spring semester - February or March. You can send an email around to various professors explaining you are interested, or stop by one of their offices and