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Fiscal Deficit is the country's earnings (from taxes, etc), less its expenses (of maintaining the institutions, welfare programmes, etc), and less the interest outflow on debt. It is typically expressed as a percentage of GDP.
Let's take a simple example – you have a good job, earning good annual increments. If you spend less than you earn, and save the rest, there is no problem whatsoever. This is like a fiscal surplus. Even if you live beyond your means for a few years, banks would be willing to lend to you, since your job and increments are good. They are confident you can pay loans back in the years to come. This is like running a fiscal deficit. Emerging countries like India regularly run fiscal deficits.
The problem arises only if this deficit rises too high – for instance you have borrowed such a large fraction of your income that banks begin to wonder how you would repay. If your salary increments stop, then too you are likely to be at risk. If banks start holding back their lending, your profligate lifestyle takes a big hit. This is one of the causes of the Greek crisis.