Inflation, in simplest terms, is the rise in the prices of commodities and services. More importantly, inflation means that money loses its value, that is we are able to buy less with the same amount of money (as compared to a scenario with no inflation). The rise in prices also results in more tax revenues to the government, through increased receipt of sales taxes, value added tax, etc. Increased prices also mean that people are getting higher incomes and thus will pay more income taxes. So overall, inflation causes increased tax revenues for the government. Since money is losing out on its value, the government has to pay less debt in today's currency.
For example, suppose the government borrows $20 billion today from the market and that inflation is 10%, whereas the yield of government bonds is 5%. After one year, the government still owes the same $20 bn (plus the 5% interest, so a total of $21 bn), however the 10% inflation will mean that the same quantity of goods will be bought for $22 bn, as compared to an year ago. This situation saves the government $1 bn. Now think of the savings in a bigger time frame, say a decade or so. Hence, inflation reduces the burden of the national debt by increasing the tax revenues and decreasing the actual real value of debt.