Read MoreArgentina's debt fight: What it is & why it matters
Several years after the 2001 default, Argentina managed to restructure the vast majority of its sovereign bonds with investors, persuading them to take just a fraction of the full amount they were then owed (a discount known as a "haircut," in this case, of 70 percent). Those investors, who swapped their original bond agreements for new ones, are referred to as the "exchange" bondholders.
But a few hedge funds, notably NML Capital, a subsidiary of the New York based Elliott Management, and a smaller fund called Aurelius Capital, refused to agree to the amended terms. These "holdouts" took Argentina to court, and through a series of lawsuits, won judgments against Argentina for the full amount they were owed from the bonds, plus interest—a total of more than $1.5 billion.
Read MoreBond holder slams Argentina's 'broken promise'
Until late on Tuesday, when Argentina's finance minister made a surprise appearance at a meeting with the holdouts in New York City, the country's officials had simply refused to even attempt a settlement with the holdouts. President Cristina de Fernandez Kirchner has called the holdouts "vultures," their demands tantamount to "extortion." Moreover, the administration is worried about the so-called RUFO clause, or "rights upon future offers" clause, in the revised contracts they struck with the exchange bondholders. Under the RUFO clause, if the holdout investors are paid in full, their counterparts who took the haircuts could demand to be paid along similar lines as well.
Q: What's the timeline of events here?
A: Argentina had until June 30 to pay what it owed to the exchange bondholders, which was about $539 million in interest. The country dispatched that money to Bank of New York Mellon, which handles the exchange bonds, in June—but after a U.S. judge ruled that the holdout creditors had to be paid about $1.33 billion (the original amount NML and others were owed, before interest) in tandem with the exchange creditors, something Argentina was loathe to do, the situation hit a stalemate.
There was a 30-day grace period associated with the June 30 deadline, which elapses at the end of the day Wednesday. Barring a last-minute change in the judge's ruling, Argentina is almost certainly headed for a technical default of its bond-payment obligations at 12:01 on Thursday morning.
Read More3rd time unlucky: Argentina set for new default
Q: How will we know when Argentina is in default?
A: If there is no change to the judge's ruling overnight, the "trustees," or handlers, of the Argentine sovereign bonds (which include Bank of New York as well as other custodial banks) will issue notices sometime Thursday morning that the bond payments in question are now past their due dates. That may be the first third-party notification of default. Still, there is likely to be continued rhetoric from Argentina to suggest that because it posted the payments it owed to the exchange bondholders on time, it is not in default. Rhetoric also could come from NML and other holdouts that Argentina has operated in bad faith and has, indeed, reached default.
Q: What is the significance of all this to the broader markets?
A: Argentina's main stock index, the Merval, has gyrated in response to recent legal events, and some of the sovereign bonds in question, which carry a yield of 8.25 percent come due in 2033, have moved sharply as well. YPF, Argentina's national oil and gas company, will also be affected by the news; it is a widely used vehicle for investing in the country's growth, or lack thereof, and its borrowing costs will likely rise if Argentina defaults. Argentinian savers, who have been withdrawing money from domestic accounts in recent years and converting their money into U.S. dollars as a bet on a stabler currency, may be tempted to pull yet more funds.
The unique legal issues at play in Argentina and the sheer paradox of a solvent country entering default has created lots of intrigue for the international markets. Some investors who focus on distressed debt, or borrowers who operate under financial duress (as Argentina was until fairly recently), have followed the saga obsessively.
However, the broader market considers Argentina's problems to be idiosyncratic and unlikely to set much precedent for the rest of the world.
Q: What exactly will happen when the clock strike 12 if no deal is reached between the group of holdout hedge funds and the embattled country?
A: The official call will be made by the ISDA determinations committee, which is made up of 15 individuals, 10 sell-side, five buy-side, from all different financial institutions. Normally, after the grace period is breached, a market participant who holds the credit default swaps contract will put a request forward to the determinations committee. Once that is done, a four-step process is triggered:
1) The determinations committee will meet and review publicly available information to determine whether a credit event, a default, has occurred
2) The committee will vote on whether or not they think a credit event has occurred. A super majority (12 out of 15 votes) is needed for the vote to pass.
3) If it's determined that a credit event has occurred there will be an auction to determine the value of protection, or how much the CDS holder will get paid. For Argentina, the CDS exposure, or amount paid out to investors, is about $1 billion.
4) Investors who insured their Argentine debt are paid out
However, this process only applies to those that insured their Argentine debt—for bondholders who decided not to insure, there won't be an "official" default call, there just won't be any payment from Argentina into their bank accounts.
—By CNBC's Kate Kelly, with Dawn Giel