By this time most of us have heard of probiotics -- living microorganisms that are beneficial when ingested. Prebiotics are closly related; they are non-digestible substances (usually some form of soluble fiber) that stimulate the growth or activity of probiotic microorganisms.
"A prebiotic is a selectively fermented ingredient that allows specific changes, both in the composition and/or activity in the gastrointestinal microflora that confers benefits upon host well-being and health."
-- Marcel Roberfroid
The most common prebiotics are saccharide polymers (oligosaccharides and polysaccharides), short chains of simple sugars that are only partially digestible by humans. These include fructooligosaccharides and inulin, which are fermented by the microflora in the large intestine, lowering the pH (and incidentally, helping certain nutrients to be absorbed by the intestine). The correct pH balance is important to encourage certain bacteria to grow. This interaction can be very subtle; galactooligosaccharides are present in breast milk (and are now added to baby formula) to help encourage the bacterial species specific to infants. In all these cases, the bacteria in question are most often of the genus Bifidobacterium, but there are different species; genus Lactobacillus also benefits from these prebiotics, as do some others, but Bifidobacterium appears to be the dominant probiotic gut bacteria in humans.
Oligofructose is considered a 'short-chain' prebiotic, and contains just two to eight links per saccharide molecule; they ferment comparatively quickly, in the first half of the large intestine. 'Long-chain' prebiotics such as inulin contains up to 64 links per saccharide molecule, and lasts longer, not breaking down properly until later in the digestion process. You can also find foods and supplements, such as 'Oligofructose-Enriched Inulin', which include chains of various lengths to nurture the entire colon.
It is obviously efficient to have prebiotics and probiotics delivered together, so you may also see the term 'synbiotics' to refer to foods or supplements that provide both. The term 'functional foods 'may also be used, although this is a general term that would also cover any foods with added vitamins and minerals.
A couple of noders have messaged me to mention that prebiotics, in high doses, can cause gas. This is true, and probably indicates that you are getting more prebiotics than you need (although you might be getting too much of only one type). Keep in mind that other things also cause gas, so don't jump to any unwarranted conclusions about how healthy you are being... However, artichokes and jerusalem artichokes do contain a lot of both inulin and fructooligosaccharide.