The most likely explanation for what you have encountered is that these are the roots of a tree or shrub that is growing in your yard or a neighbor’s yard. Roots of trees and shrubs commonly extend 2 to 3 times as far as the branches extend, sometimes considerably farther. Roots of trees and shrubs are usually fairly shallow, often with a large percentage of the roots in the top one foot of soil. Roots of trees and shrubs will tend to proliferate in areas that receive irrigation and fertilizer, like landscape beds.

If you are trying to protect an area like a flower bed from these invading roots you may have some success by creating a vertical barrier with sheet metal or a root barrier fabric.
See this for more information:

http://hort.ifas.ufl.edu/woody/rootgrowthbarriers.shtml