Most people use the word “profit” to mean “accounting profit” or “net profit”, which is the seller’s revenue (the amount he can get for all of his goods or services) minus his production costs (the money he spends to produce his product). However, when economists use the word “profit”, they most likely mean “economic profit”. Economic profit is a seller’s revenue minus his production costs AND minus his opportunity costs, which is the amount of money he could have made if he had produced anything else. In other words, economic profit is the accounting profit for one good minus the accounting profit of the good that would have made him the most money had he produced it instead.
To better understand this, let's imagine there's a town where everyone makes either necklaces or bracelets. Every necklace costs the same as every other necklace, and every bracelet costs the same as every other bracelet. Bob spent $30 on enough metals and beads to make ten necklaces or ten bracelets, either of which will take him an hour to make. He makes ten bracelets, takes them to the fair, and sells them all for $15 each. His accounting profit is:
$15 x 10 bracelets - $30 = $120
(Price x Quantity - Production Cost = Accounting Profit)
But while at the fair, Bob realizes that necklaces are selling for $20. This means that if he had used his time and supplies to make necklaces, his accounting profit would have been:
$20 x 10 necklaces - $30 = $170
Thus, the opportunity cost of not making necklaces is $170. So Bob's economic profit is:
$15 x 10 bracelets - $30 - $170 = -$50
(Price x Quantity - Production Cost - Opportunity Cost = Economic Profit)
If Bob is reasonable, he'll start making necklaces instead of bracelets. But as a result, at the next fair there will be more necklaces and fewer bracelets which will affect their respective prices. Because there are more necklaces, the price goes down from $20 to say $17. Because there are fewer bracelets the price goes up from $15 to say $17. Now the accounting profits for both necklaces and bracelets are the same:
$17 x 10 (necklaces or bracelets) - $30 = $140
Thus Bob's economic profit, the accounting profit of necklaces minus the accounting profit of bracelets, is zero.
When Bob makes bracelets
When Bob makes necklaces
This example demonstrates that if any seller is making negative economic profit selling some good, it means she could be making more money producing some other good, so she'll switch to making the other good. By the same logic, if any seller is making positive economic profit selling any good, other people will start producing that good, which will drive the price down until everyone's economic profit is zero. Thus, zero economic profit is called the "normal profit".
It is not normal, however, because in the real world sellers can make any number of different goods, different versions of the same good sell for different prices, and it is not easy to switch from making one good to another. So it's hard to determine opportunity cost. Still, in many markets, economic profit will hover around zero in the long run.