Primary deficit is the deficit which is derived after deducting the interest payments component from the total deficit of any budget.

In other words the total of primary deficit and interest payments makes up the total or fiscal deficit. The opposite of a primary deficit is a primary surplus.

How does this affect economic growth? (taking India as an example)

"Higher fiscal deficit in India has been one of the major reasons for higher level of inflation in the Indian economy as compared to other developing and developed nations. The cycle of high deficit and high inflation can be explained in two different ways. Firstly, high fiscal deficit indicates a high level of government borrowing that has a tendency to reduce the availability of capital. This leads to lower liquidity and consequently higher interest rates and higher inflation.

On the other hand, assuming that the government is borrowing to invest in the economy, this leads to increased spending that leads to greater money supply in the economy which can further lead to inflation if output fails to keep pace with this increased amount of spending (which has usually been the case in India). Further, to curb a rise in the level of inflation, the central bank resorts to a hike in interest rates. Thus, we see that high fiscal deficits could lead to higher interest rates and it could further fuel inflation in the economy if not checked adequately."