Hormesis is the effect of a toxic substance being beneficial in very small doses, but poisonous or even lethal in larger doses. In other words, a weak stimulus promotes what the same stronger stimulus inhibits.
The term was first used in a 1943 issue of Phytopathology by C. Southam and J. Erlich, who were describing an oak bark compound they discovered that promoted fungal growth in weak doses but strongly inhibited it in large doses. The researchers coined their term using the Greek word "hormo" ("to excite"), the same root used to create "hormone".
Common hormetic compounds include the trace elements we need in our diets, such as iron and cobalt, that can become deadly in high doses. Alcohol is another hormetic compound; studies have shown a drink a day may be beneficial to many people, but more than that can cause alcoholism and organ damage. Other common hormetics are caffeine and many medicines.
Radiation hormesis is an interesting area of scientific debate. While it's universally agreed that moderate-to-large amounts of radiation are damaging, some medical researchers are arguing that tiny amounts of radiation exposure (normally gained from natural background radiation) may actually have a beneficial effect. They base their postulation on demographic data that show the cancer and death rates for industrial workers who handle low-level radioactive materials are actually lower than the death rates of workers exposed to no radiation whatsoever.
As a final note, hormesis should not be confused with homeopathy, though the two bear some similarities, namely, homeopathy's core concept of giving the smallest dose of a medicine possible. Hormesis is science; it's a well-documented effect of certain substances. Homeopathy is a much-debated medical art that uses hormesis as part of its scientific basis. However, homeopathy is also based in concepts that have not been (or cannot be) tested scientifically or which are outright contrary to established scientific knowledge. Read the homeopathy node for further information.
References: http://whyfiles.org/020radiation/hormesis.html and http://www.alamut.com/proj/98/nuclearGarden/bookTexts/Rad_hormesis.html