Cascade Deletion in your relationships table will delete the related subrecords when the main record is deleted. See Tools\Relationships...; double-click on a connecting line for the related tables... you'll be able to edit relationships if you have permissions to do so and the relationship is editable (not greyed out)
For example a MEMBER is related to several monthly Membership payments. When deleting the Member without cascade delete, the error occurs because the payments would then not have a related record if the member is deleted. You could delete any payment though as those are not required. This is a one to many relationship example. 1 member has many payments.
IF referential integrity is established in the relationships and cascade delete is checked then when the member is deleted all his/her payment history/records are deleted as well.
I hope that helps,
Goh