Why do airliners have them?
Because passengers like them.
When you're sitting in the penalty box waiting for a departure slot and the air conditioning system is barely running the extra cool air you can get from those vents may be the only thing keeping passengers from strangling the screaming child kicking the seat.
Also a common "cure" for airsickness is fresh air -- blowing cool air over someone's face will often help with symptoms of motion sickness, and may prevent a nauseous passenger from actually vomiting.
Opening these overhead "gasper vents" and directing them at the passenger's face provides a quick way of doing this.
aviation.stackexchange.com/users/64/voretaq7
The airjet openings are connected to a long duct running along the ceiling.
Since the air volume inside the cabin is restricted, fresh air must be pumped into it constantly.
It is bleed air from the compressor section of the engine, which is first cooled and then enters the cabin via those ducts which feed all the little vents or airjets, as you call them.
Passengers can open or close them individually and direct the flow for best comfort.
The general idea is that some vents will be closed, but enough are open during every flight so the needed recirculation of air can happen.
If more are closed, the pressure in the duct will be higher, so the flow through the remaining vents will increase.
The total weight of all the cabin ducting is a minor consideration, it's only a few dozen gram per passenger.
aviation.stackexchange.com/users/1961/Peter Kämpf
The primary reason is that not everyone likes the same temperatures.
I happen to be cold-natured and like to be warm.
Other people are hot-natured and like to use copious amounts of air conditioning.
These allow all of us to stay relatively comfortable in the same cabin.
Also, when you're sitting on the ramp in the summer, it's more than 100 degrees Farenheit outside, and the boarding door is still open, you'll learn to appreciate these things quickly, especially if you've been standing in the jetway a while before taking your seat.
Personally, I usually turn mine off during flight, but I do tend to use them on the ramp and sometimes during taxi in the summer and/or unusually hot climates.
aviation.stackexchange.com/users/755/reirab
Lowest cost is king if you can get away with it.
Personal air vents provide more flexibility than if they were absent and the overall cost is lower.
If personal airjets are available then the jet temperature and maximum available flow can be set to suit people with preferences on the cold side of normal, while the mean temperature can be hotter than would suit a significant proportion of people.
If, instead, the cabin needed to be maintained at a temperature that most people would consider acceptable then, in the absence of personal vents, the whole cabin would need to be cooled to that temperature.
Some people would then feel too cold, which can be dealt with by clothing or blankets, and most people would be comfortable.
In the first case you have lower than otherwise energy use with "outliers" being addressed with airjets.
In the second case you have higher than otherwise energy use with outliers being addressed with blankets.
The energy cost of the blankets is zero but overall it still costs more this way.
FWIW
I'm an air-jet loving traveller and greatly dislike aircraft without them.
aviation.stackexchange.com/users/4371/Russell McMahon
Although probably not the primary reason airlines have them in the first place, there is another great reason to use them.
Having fresh "outside" air blow in front of you displaces the viruses/bacteria/etc.
from sick passenger's coughs and sneezes away from entering your nose and mouth.
aviation.stackexchange.com/users/7163/James Peckham
Make the passenger feel
he's in control of something.
The practical use is to fight rising temperatures and odors, but i also quite like the oxygen.
aviation.stackexchange.com/users/7183/Barry Staes
I never turn them on, but I do turn them off if I notice them. Is this a relic from the age when people lit up next to you and you wanted to blow away the smoke? The system must weigh almost a ton on a large aircraft and seems pretty unpopular and hard to maintain.
Why do passenger aircraft have the little airjets over each seat?
aviation.stackexchange.com
<aircraft-design>
aviation.stackexchange.com/questions/12356
aviation.stackexchange.com/users/935/yippy_yay
The primary reason seats have airjets on planes is that not everyone likes the same temperatures. Personal air vents provide more flexibility than if they were absent and the overall cost is lower. If personal airjets are available then the jet temperature and maximum available flow can be set to suit people with preferences on the cold side of normal, while the mean temperature can be hotter than would suit a significant proportion of people. Also a common "cure" for airsickness is fresh air -- blowing cool air over someone's face will often help with symptoms of motion sickness, and may prevent a nauseous passenger from actually vomiting. The vents are there for the comfort of the passengers. People like different temperatures and the vents accommodate people who like cooler temperatures as well as those who like warmer temperatures. Fresh air can also help with air sickness and may stop a nauseous passenger from vomiting. Another reason is that the vents help to recirculate the air during a flight. In terms of weight, the cabin ducting only amounts to a few dozen grams per passenger so this is not a significant consideration. Individual air vents also provide greater flexibility and are cheaper.
The vents are there for the comfort of the passengers. People like different temperatures and the vents accommodate people who like cooler temperatures as well as those who like warmer temperatures. Fresh air can also help with air sickness and may stop a nauseous passenger from vomiting. They help to recirculate the air during a flight.  The cabin ducting only amounts to a few dozen grams of weight per passenger so this is not a significant consideration. Individual air vents provide greater flexibility and are cheaper.