There does not seem to be a specific source of the idea. Two possible reasons are:

1) axons may make up as little as 10% of the brain cells, the rest are glia

2) Only 10% of the axons may be firing at any given time

Modern imaging methods clearly show that all areas of the brain are used, though not all at the same level under all circumstances

See: http://www.snopes.com/science/stats/10percent.asp