Rain gardens are gardens that are fed by rainfall formed streams. The streams can be natural or man made such as runoff from a roof, driveway, or parking lot. They are designed to retain water for several days, slowing it down from reaching a waterbody. They also serve to help take nutrients and sediment out of the water.
There are many sources of information about rain gardens on the Internet. The University of Wisconsin has a comprehensive guide to building your own rain garden.
Rain gardens are a win-win for homeowners and lakes. The rain runoff is probably already either eroding your hillside or pooling in any flat areas you have (or both). A rain garden (or more than one rain garden) may be the right way to address the situation.
Once you build your rain garden, the lake benefits from slower water movement and fewer nutrient spikes after storms. Residents also benefit since the rain garden creates a beautiful habitat which supports dragonflies (which eat mosquitoes) and reduces standing water (which can breed mosquitoes).
Note: do not make a rain garden near a well head. Also, do not make a rain garden within 15 feet of a house foundation.
Some links of interest for more details: