It is my understanding that a “concert tuning” is, as BoseEric stated, a very detailed and meticulous tuning done by a highly skilled technician. A concert tuning is above and beyond a normal in-home tuning… as I understand it, due to the many points of detail that are addressed.
Before I started learning to tune my own pianos, I called a local piano tech to inquire about his services… he began bragging how he could tune a piano, other than a pitch raise, in 45 minutes. I figure a thorough concert tuning may well take 2, 3, or 4 hours, depending on what is done.
And, as Rich state, a near-perfect tuning can turn sour quickly if a unison drifts flat or sharp is short order.
Also, as I understand it, a concert tech can charge a higher rate for their services, like any specialist in their field. And, they are worth it…