"Inflation tax" is a reference to the downside of governments printing more money. That is, when a government is short on funds and has a large payroll to meet, one option is to raise taxes. Another option is to print money. These are in many ways equivalent, because both inflation and taxes reduce the purchasing power of your paycheck.
Governments have a particular incentive to print extra money. Governments tend to have a lot of debt, and when inflation increases this benefits debtors (I'd rather pay a hundred dollars when the dollar is worthless than when it is worth a lot). Being able to print money means that you can pay off your debt at the same time that the dollar is worth less. This is a double win, if the situation is temporary. Of course, this has made every dollar in the country worth less, taking a cut from the pocket of every citizen -- effectively, taxing them.
It gets worse; this is not only something that benefits governments, but politicians. A politician that is coming up for reelection is motivated to show a good strong economy. A quick burst of inflation makes the economy look healthy -- an influx of new money into the economy means more spending; the realization that the money is worth less and that prices need to rise to meet the value of the goods is a little slower in coming, and if things are timed right the politician should already be reelected before the downside hits. This does not benefit the government in any way.
America is theoretically insulated from this by the Federal Reserve System, but the economic gossip mill has it that the Fed chairman Arthur Burns goosed the inflation rate for president Nixon in 1972, and that the Bush family holds a longtime grudge against Alan Greenspan for not doing the same favor for George H. W. Bush in 1992.