|Oh no, they're talking about
In politics, operational independence is basically the idea that (usually elected) officials decide what the government should be doing — or what high-level goals it should have — and then let the lower-level civil servants and managers (who are usually not elected) figure out how to do it at a detailed level.
It is generally recognised to be a very important property of a judicial system. The elected politicians make the law — and the constitution. The judges enforce the law and the constitution — in the process, figuring out how to apply them to awkward corner cases which may not have been explicitly anticipated by the politicians — but judges are supposed to disregard their personal feelings on whether the particular law or constitutional measure in question should exist in the first place. However, some judges in some countries are elected, and there have been controversies over alleged "judicial activism".
Its perceived importance in other areas of public life varies. In the UK, the idea of operational independence is applied quite widely across government, via both public-sector bodies such as QUANGOs, and the myriad of private companies who are contracted to carry out public functions.
While this may sound like a good idea (it's true that the alternative — political meddling — can introduce drastic levels of political bias into a government's functioning), the reality can be somewhat different — and it can be an extremely useful tool for the government to point the finger of blame at someone else, and thereby dissipate public anger at injustice or incompetence. (Shockingly, the UK has now reached the stage where managerial wrongdoers/scapegoats can now be re-hired for vastly greater sums in another part of the government!)
Central bank independence
A particularly clear example of operational independence is with "independent" central banks, such as the Bank of England. The Bank of England is still owned by the British government, and thus its assets (including government debt bought under quantitative easing) appear in the consolidated government accounts. However, monetary policy is implemented by an independent Monetary Policy Committee at the Bank of England, who are supposed to set interest rates in order to achieve an inflation target set by the government (which has been set at 2% for a number of years). If the inflation target has not been achieved for quite a while - which, as of 2015, it hasn't — it's too low — the Governor of the Bank of England must write a letter to the Chancellor explaining why. Though you might not think it from reading newspapers, this arrangement is relatively new in historical terms (the Bank of England has been stated-owned since it was nationalised in the 1940s, during a period when the UK had resumed the gold standard). The UK government under Gordon Brown as Chancellor, implemented central bank independence in 1997, on the basis that having monetary policy under the direct control over the government, as it had used to be, was too vulnerable to harmful short-term electioneering moves.
The flipside of this is that it is supposed to be futile to lobby the government (or indeed the MPC) for a change of interest rates. All that can be democratically influenced, supposedly, is the high-level goal — the inflation target. This is why UK politicians rarely talk openly about interest rates any more — central bank independence is taken fairly seriously in the UK.
However, even here the reality is more nuanced. The central bank governor is appointed by the government, who can select a person who they believe will vote for, and carry out, monetary policies that they approve of.
It is also odd that a member of the monetary policy committee has argued for higher rates in a UK newspaper editorial. What was she doing, lobbying herself? And if she was lobbying her fellow MPC members, why bother to do so in the pages of a national newspaper — why not just email them? And if it was just for the benefit of economics students, why not circulate the email to economics professors to share with their students? So the idea that the MPC is entirely removed from democratic control in practice seems suspect.
The independent economic commentator Frances Coppola has argued that on balance, even though the independent central bank concept hasn't fulfilled its objective of keeping the economy growing reasonably smoothly after the 2008 banking crisis – due to fiscal policy deficiencies, and in particular deficit fetishism on the part of governments – the alternative would be even worse, because then both the fiscal and monetary levers would be politicised.
Atos and "fitness to work" tests
Successive British governments have continued to outsource the work of assessing the "fitness to work" of disabled and ill people to private companies, who employ doctors to do the work. Previously, the main company carrying out this work was Atos. Some disability rights campaigners protested directly against Atos for making unfair and incorrect determinations of benefit claimants' fitness to work — determinations which were in fact overturned by the government itself in a significant number of cases. However, it can be argued that the ultimate responsibility for this situation lies with the government, who set the contractual goals (hidden, as usual, for reasons of "commercial confidentiality") and oversee the running of the contract. So, "passing the buck" to Atos could be argued to have been a very canny political strategy for the government.
However, this strategy may now be reaching its sell-by date, as (a) Atos has been replaced, and yet much the same problems continue to occur, indicating that perhaps it wasn't the fault of Atos, (b) the UK government's Department for Work and Pensions has been forced to reveal figures for the number of people who were refused benefits and then died shortly afterwards, which has focused public anger on the Department for Work and Pensions itself.