Accounting costs account only for the explicit costs incurred in conducting a business and not the implicit costs. The explicit costs include the direct costs to the company, such as employee wages, utility bills (water, electricity, etc.), raw material cost, premises cost, transportation and storage costs, etc. Since these are expenses for which bills or receipts are available, such costs can be objectively verified. In fact, accountants only account for accounting costs in the financial statement of the company. Since these expenses are already incurred, accounting costs are backward looking.
Economic costs, on the other hand, account for both explicit and implicit costs. Implicit costs is the opportunity cost in terms of revenue lost by forgoing the next best alternative, say renting out premises instead of conducting the business there. Implicit costs do not appear on the financial statements and are not objectively verifiable, since there can be a number of alternative to any given course of action. Implicit costs are forward looking, since they include the what if (say, we rented out the premises for next year instead of using it to conduct the business) scenario.
Hope this helps.