The word spectrum in this context refers to a range of radio-waves that are used for communication purposes. This includes the FM or AM radio broadcasts that you listen to on the way to work, and even other wireless forms of communication like Bluetooth and Wi-Fi. The smartphone you’re using also uses these same radio waves to transmit data, and the difference really lies in the specific frequencies in use, and of course, the technology used to convert those waves into something useful (whether that’s the voice on the radio, the SMS you read, or the webpage you load).
The one characteristic you need to understand about spectrum is frequency – that’s the number of repetitions of the wave you see in a second. You can easily understand this from the image below – the top-most wave is low-frequency, and so it repeats slowly. In the time that it makes three repetitions, the bottom-most (high-frequency) wave repeats 10 times. The high-frequency wave has obviously traveled a lot further in the same amount of time, but in a straight line, they’ve both gone as far – so the high frequency wave needs much more energy to travel the same distance. On the other hand, in the space it takes for three pieces of data in the first wave, you can fit 10 in the second, so you can pack more information into high-frequencies, in the same amount of time.
So spectrum refers to the waves that are there all around us at all times, passing through everything and this means that it needs to be regulated. If any one could broadcast signals at any frequency, there would be total chaos, and it would lead to a lot of interference, effectively rendering the spectrum useless for any kind of meaningful communication.
In a nutshell Spectrum is just the continuum of different frequencies that you can generate electromagnetic waves at, from a few kilohertz to a terahertz or more. The reason it’s a scarce resource that needs to be managed and can be auctioned is that to send data at a certain rate, you need a range of spectrum of a certain minimum width, a.k.a. bandwidth. And all the transmitters in a particular area need to be using different, non-overlapping ranges of spectrum or there’ll be interference. So there’s a maximum amount of data that can be sent.