The fiscal theory of the price level is the idea that government fiscal policy affects the price level: for the price level to be stable (to control inflation), government finances must be sustainable: they must run a balanced budget over the course of the business cycle, meaning they must not run a structural deficit.
It is an unorthodox theory, which contrasts with the usual monetary theory of the price level, where the price level is primarily or exclusively determined by supply of money.
These two contrasting views of prices may or may not contradict one another. By its proponents, the fiscal theory is seen as complementary to the monetary quantity theory. By its detractors, the fiscal theory is seen as incorrect, and either irrelevant or simply wrong-headed.
In nominal terms, government must pay off its existing liabilities (government debt) either by refinancing (rolling over the debt, issuing new debt to pay the old) or amortizing (paying it off from surpluses in tax revenue). In real terms, a government can also inflate away the debt: if it causes or allows high inflation, the real amount it must repay will be smaller. Alternatively, it could default on its obligations.
The fiscal theory states that if a government has an unsustainable fiscal policy, such that it will not be able to pay off its obligation in future out of tax revenue (it runs a persistent structural deficit), then it will pay them off via inflating the debt away. Thus, fiscal discipline, meaning a balanced budget over the course of the economic cycle is necessary for the price level to remain stable; unsustainable deficits will require inflation in future.
The theory contradicts the observed reality, which is that governments do not "pay off" their debts, but merely roll them over indefinitely (or occasionally default on them, but this is rare). Even when quantitative easing is used, it is not used to such a large extent as to pay off the national debt - or even recent national debts. "Paying off" the national debt would cause a crisis as it would suck money out of the economy and lead to a shortage of risk-free assets.