Greek debt, in the form of bonds, is an agreement between borrower (Greece) & lender - for the most part large European banks. The banks lend money and receive interest for their risk & opportunity costs. Such investments are a gamble to an unknown extent; interest is higher or lower depending on market perception.
If a borrower appears unsteady, and seems unlikely to pay, lenders withdraw what they can and refuse new loans. Borrower negotiates with existing lenders for new terms. The interest rate rises to potentially attract new money.
Lender banks take a financial hit. If their exposure were large, perhaps the bank would fail & close. But since the 2008-09 USA bailout (of many large banks, finance firms & manufacturers), it became more possible for banks to seek assistance from government and ultimately the public. Public funds might be provided to both borrower & lender, allowing disentanglement from agreements. Government can negotiate new requirements as a fee for participating. In the USA bailout, the terms were easy -- private interests got huge public subsidies at little cost, and this greatly undercut normal market mechanisms. For Greece, discussion among EU governments has steadily demanded more from private interests in exchange for new public help. A larger part of the original loan would be written-off ("haircut") and when bonds mature, lenders would rollover the funds - reinvesting in Greece.
So we have governments supporting each other, governments supporting private investors, and the common people paying the bills. A major trouble with activist government involvement is markets becoming skewed to political relationships. The process is inherently corrupt.
Blame for the scale of Greece's public debt resides with assorted Greek governments over past decades, who've hidden the scale of their budget deficits (Eurozone requirements of maximum 3% deficit were mocked).
Recognize also foremost a fundamental animosity by USA financial officials toward the euro - America has always hoped the euro would disappear and the US dollar become an unrivaled reserve currency. The UK has parallel rivalries with continental Europe. Beware financial news filtered through the lenses of Anglo-American interests; subsequent events may consistently seem illogical.
More on this will follow...
