exterior
When we purchased our house, the inspector recommended that we regrade all the ground that meets the house to ensure water is draining away properly.
If this is somewhat new construction, these might be anti-pest defense tubes. The exterior box resembles "Tubes in the Wall" pest defense system. Liquid pesticide is shot via CO2 at the exterior junction box and the liquid will travel throughout the house by means of the tubes.
http://www.pestdefense.com/taexx is an example of this sort of system.
Further Readings:
Given that someone put a gash in it with a string trimmer, its likely stucco over rigid foam insulation panels.
If there's wire mesh in there as well, it's likely a traditional multi-coat stucco finish that can be repaired using stucco repair techniques.
If there's no wire mesh, you may have an EIFS wall (exterior insulation finishing system), which is kind of insulation and finish in one. This should be repaired using products and techniques specific to EIFS.
Best Answer
I was given the same recommendation and decided it would be too much work for me to do myself. I was told to use a clay based soil to ensure that it doesn't wash away and to plant some type of ground cover (something like Pachysandra) to take root and hold onto the soil.
I'm far from a gardening expert but it seemed to be a tremendous amount of work to do without some kind of heavy lifting equipment and a few tons of dirt.