A cost incurred is a cost for which a business has become liable, even if it has not yet received an invoice from a supplier as documentation of the cost. This is an accrual accounting concept.
For example, a manufacturing operation uses a large amount of electricity during the month of January, after which the local power company bills it $25,000 for the electricity usage, which the company receives in February and pays in March. The company incurs the cost of the electricity in January, so it should record the related expense in January.
If the company had instead been using the cash basis of accounting, the cost incurred concept would not apply, and so the entity would not record the cost until it paid the invoice in March. This would introduce a two-month delay in expense recognition.