The difference between an economic profit and an accounting profit is that one takes opportunity cost into account while the other does not. In perfect competition, economic profit is not possible in the long run because economic profits will attract more firms to compete in the market.
Accounting profit is what we usually think of when we hear the term “profit.” This is the amount that is left over when you subtract all of your explicit costs from your revenue. If you have something left, you have made accounting profit. Explicit costs are those costs that you actually have to pay out to someone. For example, let us say that I am a lawyer working in a big firm and I decide to set up my own small firm. My explicit costs will be things like rent, electricity, and the money I pay my receptionist. Of course, I will expect to make an accounting profit. If I do not, my business is doing very badly.
Economic profit is different. It subtracts both explicit and implicit costs from revenue. Implicit costs are opportunity costs. In the example of the lawyer, my implicit cost for starting my own firm is the salary that I was making at my previous firm. It will be possible for me to make accounting profit without making economic profit.
If firms in a market are making large economic profits, other firms will, if possible, enter the market. When this happens, supply will increase, prices will go down, and profits will drop.