Hydraulic fracturing or "fracking" is a method of extracting natural gas deposits in shale rock using high pressure water. Fracking involves drilling, sometimes to depths of over 10,000 feet (that's almost 2 miles down) and injecting millions of gallons of water mixed with sand and chemicals at very high pressures. Horizontal drilling often occurs from the main vertical shaft. The pressurized water serves to break-up (fracture) the shale rock, releasing trapped gas deposits. The chemical additives serve many purposes, including thickening the liquid and dissolving minerals. The sand serves to keep the fissures open once cracks have been created by water pressure. Some of the water/sand/chemical mix stays in the ground after the gas has been extracted. Some has to be disposed of.
Fracking isn't new. The technology was first used in the late 1940s. But, the advent of horizontal drilling techniques in the 1980s combined with higher pressure water injection in the 1990s allowed access to previously unreachable gas deposits and started the current boom.
The downsides of fracking are mostly related to water pollution at the drill site and disposal sites. The upsides pertain to a reduction in air pollution and costs, because natural gas is cheaper and burns much cleaner than coal.
It also appears that in the future, natural gas production may be cleaner than we thought and new technologies can reduce the associated water pollution.
Here is a short article at Grist providing a nice introduction to fracking and the sources of controversy.
More here at The Economist
Here is a short article at USA Today looking at the future of the fracking boom
Here is an article at The Economist describing China's shale gas reserves.