The USGS has quite an informative press release via Geology.com and a graphic depicting how warming will affect the physical structure of the soil and permafrost in the Arctic region resulting in the release of carbon dioxide and methane.
Image: Zina Deretsky, National Science Foundation
There is still some uncertainty whether warming will result in the Arctic being a net source of greenhouse gases in the short term. Example warming could extend the growing season and this extra plant growth and the migration of the tree line northwards could end up sequestering more carbon dioxide than before. However sustained thawing and release of trapped gases over several decades may eventually overwhelm this balance and result in the Arctic becoming a net source of greenhouse gases.
Interesting statistic: Currently the Arctic releases about 50 million tons of methane per year. That might increase to several times more in the years to come. Methane is a more potent greenhouse gas than carbon dioxide, about 23 times more effective in trapping heat than CO2 on a 100 year time scale, so Arctic warming effects are a real cause for worry.