In some cases it’s the amount of data that can be moved. For example a stick of DDR4 RAM on a computer motherboard may be able to transmit/receive 50GB of data per second but this does not tell you how it is physically working, there are multiple different lines of communication working together at a lower speed to get this overall result.
In radio the bandwidth may have a more physical meaning— say an FM radio station at 90.1MHz was allowed to transmit as low as 90.0MHz or as high as 90.2MHz so the width of the “band” it’s allowed to transmit in would be 0.2MHz in that case.
It also has a meaning in audio— the frequency range of the sound that’s being produced (or recorded, or transmitted). Human ears can hear as big a range as 20Hz-20KHz. Usually less as people age.
Now radio waves are weird, they are not *actually sound*, but they carry information about sound that lets your speaker reproduce it. A 90MHz signal cannot transmit 90MHz sound, but if it can vary up and down by a certain amount, it can carry enough information to transmit (for example) 20KHz sound.
So an FM station that can (for example) vary from a center of 90.1MHz down to 90.0MHz or up to 90.2MHz does **NOT** have infinite bandwidth, it can only carry a limited amount of information. However it can carry enough to transmit a high quality audio signal, at least compared to AM radio, so the bandwidth may not be a problem and that’s why somebody would say it’s unlimited. In reality normal broadcast FM stations can only carry something like 15KHz which is not technically the highest sound that people can hear, but in reality, for most people and most recordings it sounds perfectly find.
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