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This is a somewhat complex situation, but here’s a simplification.
Actually, national debt by itself does not directly cause inflation - the effect is indirect. The primary cause of inflation is increases in wages that are not offset by increases in productivity. In other words, it costs more to make a product or provide a service, so the price goes up. Another cause is devaluation of the currency (when a country’s currency is worth less in proportion to others, all imported goods cost more). And anything else that causes prices to rise will cause inflation, such as scarcity of some important commodity. A good example of this was what happened to the price of oil in the 1980’s, which meant that the price of gasoline and heating oil and jet fuel and plastic (made out of petroleum) went up and the result was rampant inflation. Even today there is significant inflationary pressure because of increases in the price of oil, after a decade of relatively low prices.
When a country has a national debt, and most do, it has to pay interest on that debt and to repay the loans when they become due. If it has too much debt, the interest and repayment burdens become a big drain on the country’s revenues. A country can respond to this in several ways:
*** Austerity programs (higher taxes and/or lower government benefits) so they can pay the interest on the debt. Usually such programs are designed to have budget surpluses so they can pay down the debt. But this causes inflation in the sense that people pay higher taxes and get fewer government benefits, so they seek higher wages to compensate.
*** “Print money” to pay the interest. This devalues the currency because there is more of it out there than is needed to support the economy. On the world currency market, it is recognized that there is too much of the country’s currency floating around out there, so people don’t value it as much. So imported goods and commodities priced on the world market all cost more.
*** Default on the debt. This is a sign of a country that is in real trouble. Venezuela and Greece are current examples. When they default, nobody wants to lend them any more money, so they have to pay substantially higher interest on future debt, thus increasing the burden on their revenue. Or they must denominate their debt in the currency of some other country (Greece has no choice - it must denominate its debt in euros; some Venezuelan debt is denominated in dollars.) People lose faith in the value of their currency because they don’t pay their debts, so their money is devalued (if it is their own) or they have to go on very stringent austerity programs (see above) to have enough money to pay their debts.
