Productivity growth sets the non-inflationary wage ceiling. If output per hour grows 1.5%, wages can grow 3.5% with 2% inflation and unit costs are unchanged. If productivity is zero, the same wage growth is straightforwardly inflationary.
The quarterly series is extremely noisy because it is calculated as a residual between output and hours, both of which are revised. Trends only become visible over several years, which is why claims about a productivity boom or slump are usually premature.
Example: output rises 2.8% and hours rise 1.1%, so productivity grows 1.7%. With compensation growing 4.0%, unit-labour-costs grow 4.0 minus 1.7 = 2.3%, close to what a 2% inflation target tolerates.
Related: unit-labour-costs, potential-gdp, average-hourly-earnings, employment-cost-index, neutral-rate