What is epsilon and why do we need it in GIS operations?
I've seen this used in the context of clustering. If two points are less than or equal to epsilon distance of each other, they are considered to be in the same location.
Epsilon equivalence testing is also frequently used in geometric algebra operations that use floating point math. As Kirk said, if two points are less than or equal to epsilon in all dimensions, they are considered equivalent.
Wikipedia provides some good background on epsilon and limit testing.