CBC is one of the 3 primary cannabinoids of the cannabis plant. When CBGA, the root cannabinoid and precursor to all other cannabinoids, is created by the cannabis plant, enzymes in the plant will convert the CBGA into one of 3 major cannabinoid  acids, THCA, CBDA and CBCA.

CBCA then converts to CBC through decarboxylation (just as THCA converts to THC and CBDA converts to CBD).
Just as THC can then degrade, through oxidisation to CBN, CBC will degrade to CBL.
In its neutral form, CBC possesses anti inflammatory properties (common among both cannabinoid acids and neutral cannabinoids) as well as anti microbial properties. It has mild analgesic effects and also appears to possess significant anti cancer effects, though this is not as well established or seemingly as potent as THC or CBD. CBC is also being investigated for its ability to aid bone growth and repair.
The anti inflammatory properties are relatively well established and it is considered to have considerable anti microbial properties.
http://www.ncbi.nlm.nih.gov/pubmed/19729208

The applications for pain relief are not particularly well studied but mechanisms for possible benefit in this area, as well as others, has been observed.
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3041249/?tool=pubmed

CBC has a lot of promise but is drastically understudied at this time, even compared to other cannabinoids. At this time it has established anti inflammatory and anti microbial properties, with some mild analgesic properties and potential anti cancer, neuro protective and bone stimulating properties.