Why is inflation uncertainty important?

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Economists can never be absolutely certain. Something so complex as human activity cannot be predicted with pinpoint accuracy, so economists operate within reasonable ranges. Having a 2% inflation target really means that anything from 1% to 3% is (for practical purposes) on target and investors, are likely happy assuming “2%” if inflation remains in that range.
Inflation uncertainty occurs when something causes investors to have less confidence that inflation will stay within acceptable ranges. In that situation, investors demand an insurance payment to offset the risk. That has economic significance.
Simplistically, that uncertainty means that in addition to bond yields needing to compensate compensate for a real rate of return and expected inflation, investors will demand more money to cover the risk that inflation exceeds the forecast range.
Inflation uncertainty risk increases the real borrowing cost for the government, which makes reducing deficits and debt levels more difficult. It increases real borrowing costs for the corporate sector, affecting investment and thus growth. It also increases real borrowing costs for households, affecting consumer spending (and potentially housing). Finally, because investors are naturally risk averse, once introduced, inflation uncertainty risk can take years to remove from the economy. The inflation uncertainty originating in the 1970s took over 20 years to be removed.