From what I've read, transmitting data over the Internet for example, requires the transmitting device to distinguish 0's from 1's, if you will. I gather that having more bandwidth, i.e., having more frequencies with which to work, means being able to build a wave form, coded as a "1" for example, more quickly than would be the case with fewer frequencies available. Is this the _physical reason_ why greater bandwidth translates into being able to transmit more bits per second.
I think the previous answer is geared towards channel allocation and not bit rate vs bandwidth. I will try to clarify the issue.
First, you must understand how FM works and how a digital signal converts to FSK (frequency shift keying). Therefore I will use a simple example.
Each bit takes up some frequency. For example, the bit '1' could take up 5 Hz carrier frequency on the bandwidth spectrum and '0' could take up 6 Hz on the bandwidth spectrum. Therefore, there is a seperation of 1 Hz between bits.
If I send a '1' followed by a '0' then on a meter I should see 5 Hz frequency and then a 6 Hz frequency back to back. We could speed this up to infinity and therefore have these 2 frequencies transmitting all data at infinite speeds.
In the real world however, a '1' may fall around the 5 Hz frequency but not exactly on it. It may be about 5 Hz. Why around 5 Hz and not exactly on it every time? Because in the real world we have noise in transmission lines. Noise can distort the frequency causing it to be a little less than 5 Hz or a little more than 5 Hz. Imagine if the '1' bit is transmitted but on the receiving end it ends up received as 5.5 Hz. What happens now? It's not quite 5 Hz and it's not quite 6 Hz. Noise caused it to move 0.5 Hz away from 5 Hz. It is in the middle of 5 Hz and 6 Hz.
Now the receiving end has to decide if this is '1' or '0'. What are the odds the receiving end gets it right? By slowing down the speed the 1s and 0s that are transmitted , you can hold steady the 5Hz or 6 Hz for that bit. The faster you go, the less accurate the bit will fall exactly where it should on the frequency.
So, what are some possible solutions? Well, you can slow the frequency down or make the frequency separation larger. For example, make a '1' be 5 Hz and make '0' be 10 Hz. Now you have 5 Hz separation between bits instead of 1 Hz separation. Now if the frequency of 5.5 Hz is received, the receiving end can determine that this should have been 5 Hz. It's highly unlikely it was originally transmitted at 10 Hz. Therefore, the receiving end detects a '1'.
But what have you lost by doing this increase in frequency separation? You have taken up more bandwidth. Every cable has only so much bandwidth and if you have several channels on a cable all transmitting at the same time, you need to limit the amount of bandwidth each channel takes up or you will run out.
So, therefore, since most companies don't want to backdown on speed to the consumer (you), then they upgrade their technology (i.e. cables) to higher bandwidth cables such as fiber optic cables.
I hope this helped. Others, please feel free to expand on this topic. I've only discussed FSK modulation. Other techniques such as PSK, ASK, QPSK, bit stuffing, NRZI, CRC, and FEC codes can improve bit rate over channels.
You can read more about bandwidth limits. Shannon and Hartley came up with a theorem which still holds today and is used quite extensively. I even know someone who worked with Shannon at Bell Labs back in the day. Shannon's theorem is C = BW*log2(1+S/N) where C is the channel capacity in bits per second, BW is bandwidth, S is the signal power and N is the noise power.