A more thorough explanation:

A collateral line is a line of descent that connects individuals who are not directly related to each other as ancestors or descendants, but who share a common ancestor.

For example, if John and Mary are siblings, their children are in the direct line of descent. However, if John and Mary's cousin, Tom, has children, those children are in the collateral line of descent because they share a common ancestor (John and Mary's grandparents) but are not directly related as ancestors or descendants.

Collateral lines can be important in legal matters such as inheritance and property rights.