NAIRU is one of those nasty looking acronym beloved by economists. Typically, the concept works very well in theory but has an unfortunate tendency to breakdown as soon as you apply it in the real world. It kinda makes sense that if there is a sufficiently large pool of unused labour in the economy, wage inflation will remain under wraps. Only once that spare capacity is used up do workers have the power to claim higher wages which are in turn passed on in higher prices.
Contrary to what the term suggests, an economy running at "full employment" still has unemployed workers within it. There are always workers in between jobs and seasonal workers who aren't currently employed. As a rule of thumb, 2-3% of all workers find themselves in this situation at any one time. Beyond this, there is an additional pool of workers who don't have the requisite skills required by employers. Skin heads tattooed with "YOUR" and "NEXT" on their knuckles are unlikely to find employment at a bank for example. Economists politely term such individuals as the 'structurally unemployed'. With sufficient training, and presumably a little plastic surgery, they'd be good to go as a cashier or whatever.
Unfortunately, the NAIRU theory starts to breakdown at this stage as no one knows what the structural unemployment rate is and without it, the Non-Accelerating Inflation Rate of Unemployment can only be guessed at. While economists may have more practice at it, they don't seem to be better at guessing than anyone else.
Returning to the real world, this presents a real quandary for central banks. In the UK, employment levels have reached an all time high of 74.8%, yet last year the Bank of England loosened monetary policy and wage pressure still remains muted. In the US, unemployment has fallen to 4.3%, yet the Fed is only making tentative moves to lift interest rates. Policy 'remains accommodative, according to Yellen and this seems completely out of sync where history suggests it should be.