As we know Bill Weasley works as Curse-Breaker for Gringotts in Egypt.
Gringotts is a bank. Which part of their business would require a Curse-Breaker?
Speculation, but I'm not sure there's any canon answer.
We know that whatever "curse breaker" is an active, in the field job. We know this from Order of the Phoenix.
"Is Bill here?" he asked. "I thought he was working in Egypt?"
"He applied for a desk job so he could come home and work for the Order," said Fred. "He says he misses the tombs, but;" he smirked, "there are compensations."
We can also infer it's likely related to the "cursed" Egyptian tombs, not only from the above quote but from Prisoner of Azkaban.
It's amazing here in Egypt. Bill's taken us around all the tombs and you wouldn't believe the curses those old Egyptian wizards put on them. Mum wouldn't let Ginny come in the last one. There were all these mutant skeletons in there, of Muggles who'd broken in and grown extra heads and stuff.
So it seems the tombs really were cursed by ancient wizards.
Final piece of lore that helps flesh this out - Goblin ownership.
"However, there is a belief among some goblins, and those at Gringotts are perhaps most prone to it, that wizards cannot be trusted in matters of gold and treasure, that they have no respect for goblin ownership."
"I respect --" Harry began, but Bill shook his head. "You don't understand, Harry, nobody could understand unless they have lived with goblins. To a goblin, the rightful and true master of any object is the maker, not the purchaser. All goblin made objects are, in goblin eyes, rightfully theirs."
"But it was bought --"
"-- then they would consider it rented by the one who had paid the money. They have, however, great difficulty with the idea of goblin-made objects passing from wizard to wizard. You saw Griphook's face when the tiara passed under his eyes. He disapproves. I believe he thinks, as do the fiercest of his kind, that it ought to have been returned to the goblins once the original purchaser died. They consider our habit of keeping goblin-made objects, passing them from wizard to wizard without further payment, little more than theft."
Given the Goblin notion of ownership (aka the owner of an item is the crafter, everything else is a loan) that, as well as raiding ancient areas for gold, it's possible that Gringotts mounts regular excavations to "retrieve" Goblin artifacts buried with wizards or muggles.
Regardless, it seems pretty clear that Bill's most likely job is exploring ruins and "defusing" any traps (curses) left by ancient magical kind.
A Curse-breaker basically makes sure that tombs and ancient sites are safe before Gringotts takes gold from it.
Here's what the pamphlet that Gringotts gives out to fifth years says:
Are you seeking a challenging career involving travel, adventure, and substantial, danger-related treasure bonuses? Then consider a position with Gringotts Wizarding Bank, who are currently recruiting Curse-Breakers for thrilling opportunities abroad!
And here's what the wiki says:
A Curse-Breaker is a profession at the wizard's bank Gringotts, in which a wizard or witch disables or counters curses in ancient tombs or other historical sites, in order to bring back gold to Gringotts. It is speculated that Curse-Breakers are almost the equivalent of Muggle archaeologists.
I know there's a quote from Ron in one of the books that says exactly that. As soon as I find it, I'll put it here. (see @ibid's answer for that)
From Ron's letter to Harry, we can assume that curse breakers remove curses from old tombs to extract the gold.
It’s amazing here in Egypt. Bill’s taken us around all the tombs and you wouldn’t believe the curses those old Egyptian wizards put on them. Mum wouldn’t let Ginny come in the last one. There were all these mutant skeletons in there, of Muggles who’d broken in and grown extra heads and stuff.
(Prisoner of Azkaban, chapter 1)
Book of Spells goes further, and equates curse breakers with treasure hunters
The Gouging Spell enables a witch or wizard to carve through earth and stone with ease. From budding Herbologists digging for Snargaluff seedlings to treasure-hunting curse breakers uncovering ancient wizard tombs, the Gouging Spell makes all manner of heavy labour a matter of pointing a wand.
(Wonderbook: Book of Spells)
Besides breaking the curses in old tombs, I would guess just regular banking business could make use of a curse-breaker.
The bank might often need to collect valuables which they have the legal right to, but their owners might be reluctant to give up. Imagine that you owe the bank a nice sum of money, be it from accumulated fees you didn't pay, or because of a loan. They win a case against you, and you know that collections agents will show up soon so that you have to give up money or a nice golden family heirloom if you don't have enough money. Wouldn't there be a temptation to put a curse on it? I would guess many real-life muggles would want to put a curse on such things if they had the means to do so.