Structural Inflation refers to a situation of rising prices as a result of expansionary monetary policy i.e. the creation of new money. Extra money circulating in the economy creates extra demand for goods and services relative to their supply, and this creates pressure for prices to rise via market forces.
The term is intended as being distinct from demand-pull inflation (or cost-push inflation), even though the extra money created rising prices via stimulating demand. The point is that demand can rise or fall in the short term irrespective of monetary policy, so structural inflation is a unique phenomenon, and is just one pathway that can lead to demand-pull inflation.
Some controversy arises over the use of this term because it can be argued that it obscures the original meaning of the term inflation. I'll briefly explain this next.
In its original use, inflation did not directly relate to a situation of rising prices in the economy. Instead it simply referred to an expansion of the money-supply. Rising prices were then seen as being a natural consequence of 'inflating' the money supply.
If inflation is a term that describes an increasing money supply, describing the resulting price level increase as structural inflation is somewhat confusing i.e. is 'inflation' used to describe expansion of the money supply or a rising price level? The same word should not be applied to two different meanings.
Of course, the meaning of words can change over time, and this is nothing new. At one time a Xerox machine meant a photocopier produced by the company Xerox. However, since the term became synonymous with photocopiers over many years, Xerox machine simply came to mean photocopier. The company actually lost its copyright of the term!
However, controversy still exists over the correct use of the term inflation, and that's because it has been manipulated by the government for self-serving means.
The reason why some economists object to terms like structural inflation is because of the way in which it allows the government to shift the blame for causing prices to rise.
Everyone knows that the government (or the monetary authority i.e. Federal Reserve Bank) is responsible for monetary policy. That being the case, everyone knows that the government is accountable for any expansion of the money supply.
If the term inflation is used in its original sense then all inflation is structural, and the government is responsible for the resulting price increases and extra costs of living. By disassociating the term inflation from meaning an expansion (or contraction) of the money supply, and instead relating it directly to rising (or falling) prices, the government can shift the blame for rising prices onto businesses.
They frequently refer to 'price gouging' on the part of greedy capitalists who are profiteering from the price increases, and they do this even after causing huge increases in the money supply.
I'll leave it to the reader to decide whether or not the term structural inflation is an appropriate term or a manipulation, but it helps to be aware of these controversies.