Probiotics are live, naturally occurring microorganisms that have a beneficial effect in the prevention or treatment of specific medical conditions. Added to foods after pasteurization, they do not cause disease—they actually can help to treat it.
Prebiotics are ingredients which are not digested (and therefore have no calories!) that somehow selectively stimulate the helpful internal growth of specific microorganisms and create a helpful, probiotic effect.
Specific probiotics turn out to be good for specific conditions. For example, Lactobacillus acidophilus in yogurt helps improve calcium absorption; Saccharomyces boulardii improves the diarrhea some people get from antibiotics; Lactobacillus rhamnosus improves infant diarrhea caused by a virus; Streptococcus thermophilus improves lactose intolerance; Bifidobacterium bifidum helps healing of stomach ulcers, after antibiotic therapy to eradicate H. Pylori…the bacteria that caused them! A free full text scholarly review from French scientists is here.