The definition of post-industrial economy is that the service sector generates more GDP than the manufacturing sector, that's all it is.
The main issue are that (1) there's only so much food you can or should eat. After that, increased agricultural output can't improve your standard of living. Hence, the shift to industry making other goods that you need to live. But (2) once industry can make all the basics, is hoarding more "stuff" going to automatically improve your standard of living? You hit a point where you own so much "stuff" that getting more "stuff" is detrimental instead of beneficial. Yet would you say life literally can't be better than it is now because you have more stuff than you can use?
At this point, the limiting factor is no longer how much food you have to eat, nor how much junk you have crammed in your house, you have a good enough car, too. At this stage the limiting factor on most people's lives is time. And that's where services come in. You pay for services so that you can enjoy the free time that you have. Medical care grows as a proportion of spending as people live longer due to abundants no longer being constrained by food and goods. And medical care is part of the service/knowledge economy.
Also, the knowledge component of all production processes is continuously increasing. It's knowledge that makes productivity increases possible. Improved knowledge becomes more cost-effective than throwing extra manpower at a problem, hence resources get shifted to R&D, which is part of the service economy.
And that's what post-industrial society is all about. We hit the point where, just like excess food from agricultural productivity increases, we have excess industrial goods from industrial productivity increases. And the only way to value-add is to generated knowledge. Yet we still have growing incomes and we need to spend it on something else.