In his Autumn Statement speech, the UK chancellor Philip Hammond talked about the UK falling behind in productivity. He made the comment that "...it takes a German worker 4 days to produce what we make in 5".
Productivity matters because it drives what we earn. A nation with higher productivity will be able to pay a higher real wage.
The first point to make here is that it is the average that matters. So, nobody is claiming that for example, that it takes a British hairdresser 25 minutes to cut one head of hair, when it only takes a German hairdresser 20 minutes. And the average is what matters for pay. Hairdressers in rich nations earn more than those in poor, because overall productivity in those nations is higher. Not because they are quicker at cutting hair.
So, whilst there are some areas where productivity is the same in different nations, there are others where it will be different. So, maybe in the car industry for example, German workers are producing more cars per day than British workers.
Now, this may be the case. But on the whole, it is not so much about quantity as quality. Productivity growth tends to arise not because we learn how to make more off the same stuff with less effort, but because we develop new and better products. We have better televisions than we had 50 years ago; not simply more of the same old model.
It may not be so much that German workers produce more cars in a given period, than that they produce better cars in that period. And in practice, being "better" simply means commanding a higher price. (Productivity is derived from volume measures of output, which have to use estimates for the relative quality of new or improved products. These estimates are often based on relative price.)
Therefore, what Hammond's comment means is that the output of the average German worker sells for 125% of what the average British worker's output does. Fixing this comes not making more of the same thing per day, but from making stuff that is in higher demand and sells for more. Positioning in international trade is a key part of this.