Rain gardens are also known as recharge gardens.A rain garden is a planted depression that allows rainwater runoff from impervious urban areas like roofs, driveways, walkways, parking lots, and compacted lawn areas the opportunity to be absorbed. This reduces rain runoff by allowing stormwater to soak into the ground (as opposed to flowing into storm drains and surface waters which causes erosion, water pollution, flooding, and diminished groundwater).They can be designed for specific soils and climates. The purpose of a rain garden is to improve water quality in nearby bodies of water. Rain gardens can cut down on the amount of pollution reaching creeks and streams by up to 30%.
In urban areas, generally the natural depressions are filled in. The surface of the ground is leveled or paved, and water is directed into storm drains. This causes several problems. First of all, streams that are fed by storm drains are subjected to sudden surges of water each time it rains, which contributes to erosion and flooding. Also, the water is warmer than the groundwater that normally feeds a stream, which upsets the delicate system. Warmer water cannot hold as much dissolved oxygen (DO). Many fish and other creatures in streams are unable to live in an environment with fluctuating temperatures. Finally, a wide variety of pollutants spill or settle on land surfaces between rain events.
Rain gardens are improve water quality by filtering runoff, provide localized flood control, aesthetically pleasing, and provide interesting planting opportunities. They also encourage wildlife and biodiversity, tie together buildings and their surrounding environments in attractive and environmentally advantageous ways, and provide significant partial solutions to important environmental problems that affect us all.
The first rain gardens were created to mimic the natural water retention areas that occurred naturally before development of an area.A rain garden provides a way to use and optimize any rain that falls, reducing or avoiding the need for irrigation. They allow a household or building to deal with excessive rainwater runoff without burdening the public storm water systems. Rain gardens differ from retention basins, in that the water will infiltrate the ground within a day or two. This creates the advantage that the rain garden does not allow mosquitoes to breed.
A Word of caution
If built incorrectly, rain gardens can accumulate standing water or increase erosion. These problems can be avoided by following published design guides.
Link and Sources:
Download A Good Presentation on the Subject
Read more Here
Rashid's Blog: Portal for Inquisitive Learners 
Pingback: Urban Systems in India: Definitions | Rashid's Blog