Pasteurization works the same with eggs as it does with milk - they're heated to kill micro-organisms that might be potentially harmful. Pasteurizing doesn't kill everything, but significantly reduces salmonella and other micro-organisms. If your recipe specifically calls for pasteurized eggs, I'd bet it's because the yolks won't be completely cooked in the preparation, which wouldn't kill all the bacteria or other micro-organisms that may be present. The FDA requires all store-bought eggs in the United States to be pasteurized.
However, pasteurization is a process that came along after milk (and eggs) started to be mass-produced in large farming operations, instead of individual family farms. Keeping hundreds or thousands of animals all together in the same place increases the amount of bacteria those animals are exposed to. The practice of treating industrially raised animals with antibiotics (to reduce deaths from the extra germs they're exposed to) kills the weak germs, but actually allows some germs to become stronger and resistant to those antibiotics (and therefore more dangerous for people to consume them), which makes pasteurization all the more necessary.
A lot of people, including myself and the majority of small family farmers, believe that when animals are kept in a healthy environment (i.e. NOT in large confinement facilities full of poop and sick animals), and are healthy themselves, the risk of food-borne illness like listeria and salmonella is slim to none, making pasteurization unnecessary.
SO, it really is a matter of how germ-phobic you are, and how confident you are in the health of your birds. I frequently make hollandaise sauce, runny over-easy eggs, carbonara and other things with un-cooked or under-cooked eggs from my chickens. I'm confident in the health of my birds and the safety of their eggs. (I wouldn't eat them RAW, but that's another thing altogether.)