Accounting profits simply take a firm’s total revenues and subtract from that all of the costs that it actually pays out to people. These costs are called explicit costs. In the example above, the explicit costs are the helper’s salary, the rent paid, and the materials he bought. All of these things were actually paid for.
By contrast, economic profits are the accounting profits minus all the opportunity costs of the business. These opportunity costs are things the owner of the business gives up in order to run the business. In the case given here, the implicit costs are the money that John could have earned by investing (the $4519), the $15,471 he could be making working for someone else, and the value of his entrepreneurial talents.