The government levies taxes (demands money at the point of a gun) to finance expenditure (i.e. pay for things).
The budget is a plan for how much money the government will raise and how much it plans to spend in a particular year. The government says “we will put taxes on these people” and “we will put taxes on these transactions” and guesses how much money that will bring in. And the government says, “we will hire these many police officers” and “we will defend this border” and “we will give every household six LPG cylinders” and guesses how much money that will cost.
The deficit is the difference between what the government plans to spend and the total amount it plans to raise. In other words, the fiscal deficit is how much the government plans to borrow that year, because it has spending that it cannot finance through taxes and other sources of revenue.
The debt is the accumulated borrowings. If the government borrows ₹5 every year for ten years, the fiscal deficit is ₹5 every year, and the debt at the end of those ten years is ₹50.
Debt is not necessarily bad. An elementary notion in finance is that one thinks about the cost of capital in relation to the expected return on your investment. You want to borrow for less than you eventually hope to make back. Borrowing is not inherently bad. This is plainly intuitive if you understand the idea of a business loan.
You need comparators. Now, the absolute number of ₹50 is not very useful, because it is a very different thing for me to have ₹1 lakh in debt and for Mukesh Ambani to have ₹1 lakh in debt. Our ability to repay depends on how much money we make. And so it makes no sense to represent our relative indebtedness by saying we both owe ₹1 lakh. We solve this by representing the number as a fraction of something else. We add a denominator.
In this way, we can compare the situation in various states and countries.
The GSDP is a useful denominator. The Gross State Domestic Product (GSDP) of Tamil Nadu is an estimate of the value of things made and services provided in Tamil Nadu during a given financial year and so we can express the debt as a percentage of the GSDP. This gives us a better picture of the fiscal position.
Tax revenue is another useful denominator when you want to understand repayment pressure. If you want to understand how burdened a government is by its borrowings, divide the debt by its tax revenue instead. A government that owes ten times its annual tax collection is in a very different position from one that owes three times its annual tax collection, even if their debt-to-GDP ratios look similar.
The thing I am trying to get across here is that these ideas are remarkably simple. You really can, and should, be thinking about how well your government is doing at fiscal management.