To be honest I can not think of many cases where I would create 2 tables and the child table would have exactly ONE record for every parent. Generally there are multiples or I would just create a single table with all the fields in it.
Customer -> Products is a classic example of 1 to many.
If you don't find the need for that, then you don't need inheritance.
But if you want t business case, I'll try to think of one for you.
Here you go.
Suppose you have a Customer table with all Customer related fields.
But your system requires a special treatement for VIP Customers, you need more fields only used for VIP Customers.
Then you have 2 options:
Add these fields to the Customer table, and for normal Customers, these fields would be set to null. You might also need a field/flag to tell you if this Customer is VIP or not.
Another option is to move these extra fields into another table.
And a record of a VIP Customer in the Customers table would have a corresponding record in the VIPCustomers table as an extension, to hold values for the extra fields.
A normal Customer wouldn't have the extension record in the VIPCustomer record.
Thus to say for each record in the Customer table, there can be 0 or 1 related record in the VIP Customer table. (1:1) relation.
You can call this an inheritance relation, since a record in the VIPCustomer table inherits some attributes/values from the Customer table.
You can also think of it as an extension to the original table.
But again, if you don't have the business case for it, then don't use it.