Cost incurred is a cost that a company has become liable for.
To illustrate, let's assume that a new retailer opens on September 1 and its electric meter will be read by the utility on the last day of every month. During September the retailer has incurred the cost of the electricity it used during September.
Under accrual accounting the retailer needs to report a liability on September 30 for the amount owed to the utility at that point. On its income statement for September, the retailer needs to report electricity expense equal to the cost of the electricity used during September. (The fact that the utility will not bill the retailer until October and will allow the retailer until November to make payment is not pertinent under accrual accounting.)