Productivity is a commonly used term among economic commentators, and even more frequently used in academic writings. Actually defining and interpreting it is difficult, however.
Here's a quick definition of labour productivity: it is national output divided by the size of the workforce. The definition is the obvious one, but does leave some questions open. If this quantity depends on labour itself, for instance if national output rises disproportionately quickly as the workforce gets larger, then to interpret the quantity, one may also want to specify the size of the workforce to express the full relation between workers and their production.
Then there's the question of interpretation. The phrase high labour productivity implies that workers are smarter or more diligent than those with lower productivity, and if they are, then productivity will usually be higher, other things being equal. However, economic output depends on many things besides the intrinsic qualities of workers, such as the amount of physical and financial capital in the economy. So a lazy worker in an advanced economy will generally have far higher productivity than a worker in a less advanced economy, because the advanced economy has greater non-labour productive assets.
To avoid some of the problems, economists have looked for a definition of productivity which does not depend on the common factors of production at all. If the economy is known to produce goods in such a way that output equals a constant times capital times labour force size, then we can divide output by capital times labour to get the constant, which we can label productivity. It measures the productivity of the productive factors, so that it could be considered to measure the productivity of the total economy.
There are some difficulties thrown up here, too. Economists do not know exactly what production function occurs in the economy, and any function used is an approximation. It may not even have the correct functional form. The constant will often not really be constant but depend on the factors of production, so this definition encounters the same problems of factor dependency discussed with labour. Since we are admitting that we only have estimates of the production function, and our productivity measure is inexact, we could have many different measures of productivity.
If we had a perfect knowledge of the production function in terms of the specified factors, then productivity would be interpreted as the contribution to growth of all productive factors which are not explicitly stated. Thus, once we include more productive factors, the economy's estimated productivity would vary.
Let's summarize. In commentary, productivity tells as much about the productive factors to which it doesn't refer as the ones it does, and in economic analysis, it measures how much we do not know about production.