Carbon offsetting is giving money to offset the amount of carbon you or an organization uses. People can calculate how much carbon is released into the atmosphere because of their actions at many sites like The Nature Conservatory or the Environmental Protection Agency. The money spent on carbon offsets is used on various endeavors that would reduce the amount of carbon released into the environment. Depending on the program this could be done in many ways. Putting money in renewable energy sources which include wind power, solar power, hydroelectric power, geothermal power, methane collection, and biofuels. Some of these types of offsets are used to reduce the cost differential between renewable and conventional energy production, increasing the commercial viability of a choice to use renewable energy sources. Other offsets are designed to make existing energy sources more efficient and reduce their pollution or properly dispose of the waste chemicals created. Still other types focus on land and forestry usage. Many of the practices done have secondary benefits, things like more room for wild animals, decreased energy usage, reduced energy prices, more efficient products, etc.
There are some negatives of course. Writing a check is not an excuse to not reduce your own environmental impact but some people see it as one. Some of the alternatives have negative side effects. Bio-fuel, for example, is sometimes not a good alternative to gasoline. Biofuels made from corn cause the prices of corn to go up - which has the side effect of increasing the price of foods containing corn and meat from animals that were commonly fed corn. The corn based biofuels used in the USA are made with the parts of the plant that are edible by humans and animals which means that it is not available to those humans/animals. There are plants that are more efficient than corn to use as well, some other types of grass grow much faster and taller (corn is in the grass family).
There are various ways to reduce carbon usage and there are sites online which give carbon credits for free like Care 2 which has click to donate.
Brighter Planet is currently running a campaign that will donate 136 pounds of offsets (which it estimates is the equivalent of one day's worth of CO2 emissions). I have placed on this page in the upper right corner a badge which links to this campaign. The first 25 people to click the link and sign up will offset 136 pounds of carbon each.
More info can be found on various websites like these:
Climate Crisis - the site for Al Gores movie An Inconvenient Truth.
Take Part - a site with information on things people can do
Pollute Less - another site with information about reducing carbon impact.