I've been a part of a couple of oversea's medical volunteer trips, and what I've mostly found from my own experience, and from others is that education makes the difference.
Manpower isn't so much an issue, b/c the people are there to staff clinics. The problem is the education systems are not in place to educate the staff in these clinics to provide the best care that they can. As a nurse going to a third world/developing country, you can make a big difference by bringing your knowledge of health infrastructure, new practices, education, preventative education, school lessons, etc.
While I was able to help the staff at the clinics I worked in by being a knowledgeable warm body, I was best put to use educating wherever I could. Sure, there was nothing I could teach the midwives about delivering babies, as they knew a ton about that and had done it a thousand times a year....but I educated them about changing the needle from mom to baby when giving meds/drugs. I was able to provide HIV/AIDS education to school children, who said that they believed what I said because I was an outsider.....not a local spreading myths to stop kids from having sex. In Asia I helped a local health care provider begin to set up a micro-insurance project in his local community. One of the clinic's I worked in only had one health care provider who worked 6 days a week, all year x 20 yrs, and couldn't take a day off b/c there was no one to take his place. He said he appreciated that I was able to do a majority of his work at the clinic for several weeks, while he sat, observed, and rested his feet & knees.
There are so many things nurses/nursing students can do to help, while also getting an amazing educational experience from it. If you want to learn more about what nurses can do overseas look into Doctors Without Borders
or Medicines Sans Frontieres
. Navigate through those websites and you'll find testimonials/stories from Nurses working in the field.