In an allergy, the body reacts to certain cells or molecules as if they were dangerous foreign bodies (antigens), and mounts an immune response to them - producing the typical allergic reactions like hives, vomiting etc. . The immune reaction only occurs if the blood contains specific antibodies for these specific antigens, and among them is one called ImmunoglobulinE, or IgE.
RAST is a blood test that shows if the body has IgE antibodies for particular antigens. It's not 100% certain, possibly 90% but only in the sense that if it doesn't show a reaction, there's about a 90% certainty that the child is unlikely to have an allergy to whatever is being tested. It's also only as good as whatever they choose to test - with ds1 our dietitian unhelpfully forgot to put milk or soya on the list, and instead he was tested for a variety of things including 'white beans' (whatever those are supposed to be - perhaps haricots?) so I am still not absolutely certain whether his reaction to soya is an intolerance or an allergy.
The other common test for food allergies is a skin prick test, which some specialists believe is better than a RAST, but they may not work if the allergic reaction is localised, for example in the gut rather than in the skin. (This bit of information is taken from the book 'The Complete Guide to Food Allergy and Intolerance' by Jonathan Brostoff and Linda Gamlyn, which is my 'bible'. Incidentally, both of the authors will be at the Allergy Show in London this weekend.)
Food intolerances do not show up on either of these tests, and this appears to have contributed to many doctors' refusal to believe that they are 'real' (despite the experiences of many parents). I believe the only real way you can determine a food intolerance is by doing an exclusion diet, but even if you find a medic who believes you, you are unlikely to find someone who will support you through this process (at least in my experience) which leads to many parents going through it alone, or with the 'virtual' support of other parents on the internet.
Apologies if this sounds a little like an essay, I'm currently studying human biology with the OU and my last essay was on the immune system! My study is motivated by wanting to become a nutritionist, and this in turn is motivated by the experiences my ds1 has been through (even before ds2's reaction to brazil nuts). Hence another reason I'm kicking myself for not having recognised the reaction when it happened. Just goes to show the difference between academic knowledge and 'clinical' experience!
By the way, if you want more info on the difference between food allergy and intolerance, Allergy Uk do some good factsheets. I believe children more often have an intolerance than allergy to cow's milk, so I'm wondering if this might be so in your dc's case - although of course you may have investigated it fully at the time so I'm not making any assumptions.
there's more info on allergy tests on \link{http://www.bbc.co.uk/health/conditions/allergies/testing_index.shtml#skin-prick_test\this BBC Health page}