Until recently, information on the internet was transmitted over the wires, but now information can be transferred over the air.
Since people have figured out how to use electromagnetic energy (or light) to transmit data, all sorts of radio communication devices were invented.
At first there were walki-talkis, which allowed two devices to communicate with each other wirelessly. Data can be transmitted by sending a wave between two devices at a frequency both devices are set to. This creates a wireless channel for exchange of data. Walkie-talkies could transmit on only one channel. That's why only one person can talk at a time.
Then came CB radios. They could transmit on several channels. So different communicators could set their radios to a specific frequency and talk to each other without interfering with other communicators. This allowed for several communication channels to happen at the same time.
Then came car phones. They allowed for more channels than CB radios. But not that many.
Just like with Internet Exchange Points between wired connections, there needs to be an exchange point between two wireless devices. That exchange point is a tower with an antenna, which receives data from one device and transmits it to another device.
With car phones, there was only one tower per city. Because of that, both the tower and the car antenna had to emit a lot of energy to send signals to each other.
Then the concept of a "cellular" phone was invented. Instead of having one big tower, the city is divided into many "cells" about 10 miles in diameter. Since towers were now closer all over town, the antennas on the tower and the phone didn't have to be so strong. This allowed for smaller phone antennas and phones which could be held in a hand. Because there are many towers all over town, towers which are not next to each other can reuse the same frequencies. This greatly increased the number of possible connections at any given time. So came the 1st generation of cellular phones, or 1G.
Then came 2G. It allowed to convert analog audio to digital signal, which allowed to compress the signal, and thus create a larger number of possible channels. It also allowed to transmit text messages between phones, besides just calling.
There are only so many air channels that could be created in any geographical area though. That is because there is a limited range of frequencies over which such communications would work well. A cellular service provider is a private company which has the permission from the government agency, (FCC in US), to operate in a certain spectrum of electromagnetic frequencies. To encourage competition and fair prices to consumers, the government decreed that in any given area, at least two companies need to provide cellular service. So each company is given its range of frequencies it can operate on.
Then came 3G. It allowed for even more channels and much better speeds. It became possible to transmit image, audio, and video data between devices.
Then came 4G. 4G is fast enough to allow transfer of multimedia data not only between cellular phones, but between computers as well. So wireless internet connection is available to all wireless-enabled devices now.
The wireless carriers and the FCC are on a fast track to developing the 5G network. This will allow for cable-internet speeds between wireless devices. And introduce many more towers. Besides allowing for connections between phones and computers, 5G will allow for connections between all sorts of new wireless devices called the Internet of Things, smart cars, smart houses, smart cities, smart wearables, etc.
Sources:
"How Cell Phones Work : HowStuffWorks." HowStuffWorks. N.p., n.d. Web. 04 Nov. 2014.