What is a billable expense income? could I use this category when receiving payments for works completed?

Billable expense income is when you buy something, then you mark it as being billable to a customer, and finally you invoice it.

Billable expense in the QBO+ version and has to be turned on in company settings before you can use it

In company settings turn on make expenses and items billable
check mark to track billable expenses and items as income
then in company settings>advanced>chart of accounts click the edit pencil and select the billable expense income account

Why intuit separated the two related settings is anyone's guess

When you enter a vendor bill/CC charge/etc, you will see a Billable check mark box, check that and select the customer name in the customer block. The next time you invoice your customer, the system will show billable expenses on the right side that you can click the add link to add the bill to the invoice. IF you do not want to add the bill to the invoice, leave the billable check mark box blank, the cost of the expense will still count against the customer