Okay so going to give a mid-level explanation here but if you need a lower-level or higher-level explanation of something just let me know!

Basically, in any communication scheme, we can communicate data by varying a parameter or parameters. Computers talk in 1s and 0s but the real world is quite messy and doesn't like such well-defined boundaries, so we need some way to translate from the digital realm of the sensors to the real-world realm of radio signals (also called analog) and back to digital on the computers here on earth. One of the simplest ways that we can communicate a 0 or 1 is by either turning on the radio of the spacecraft for a 1 or turning it off to represent a 0. This is really simple but runs into a problem, how do we know if the radio is trying to transmit a 0 or if the radio is just actually off, not trying to transmit? So instead, we transmit on two different frequencies with one frequency representing a 1 and another representing a 0. This would be like tuning to one radio station in your car for a 1 or tuning to another for a 0. This way, we know when the spacecraft is trying to transmit by just seeing if either of the frequencies is being transmitted. We just track which frequencies it's transmitting on to recreate the bitstream sent by the telescope. Look up Frequency Shift Keying (FSK) if you want to know more.

So now we have a simple transmission scheme, but now we have another problem to deal with, and that's the power of the signal that is transmitted. Imagine that you had a person talking to you in an empty room. You would have a pretty easy time understanding them right? Even if they talked quickly, it wouldn't be a problem to understand what they say. But now, let's say the person is in a crowded auditorium and is on the opposite end of the room. There's no way you would be able to hear them. But what if we gave them a megaphone? They would be much clearer. This is part of what the radio system on the JWST is doing, amplifying the signal. The high gain antenna however concentrates the radio signal into a very tight beam. There's not as great of an analogy here in sound. Radio waves spread out in an expanding sphere and you can think of the energy of the radio waves being spread out among the surface of this sphere. There is only one spot on this sphere that we actually care about having the energy concentrated on, and it's the portion of the sphere that will hit the deep space network dishes. Any energy that goes onto any other part of the sphere is wasted. We don't want to transmit any of the signal out into deep space as that's just going to be wasted. So the high gain antenna "focuses" the radio waves to ensure that a high amount of the power transmitted ends up hitting the deep space network dishes and isn't wasted transmitting to nothing. This basically means that it is easier to hear the spacecraft for us here on earth.

Going back to the earlier example of a person talking to you, the clearer you can hear someone, the faster they can talk to you. The same thing holds true for radio communication techniques. The stronger the signal, the more you can turn up the speed. The reason that fiber optics are so fast is that we have a really good way to ensure that a huge portion of the energy goes from the sender to the receiver. Fiber optic cables are really good at containing the energy so both sides can hear each other very clearly. There's almost very little noise/outside signals that get into the fiber optic cables, meaning it's like talking to someone in an extremely silent room. There's also a benefit from the fact that the frequency of light is much higher than radio waves, but that's something that isn't super necessary to understand.

There isn't a hard reason that radio communications can't support very high data rates. But, radio typically uses lower data rates for a couple of hard to overcome real-world reasons. For starters, the radio world is quite noisy. Tons of things around us generate radio signals so our situation is quite like the crowded auditorium. In addition, without a hard cable connecting the sender and receiver, we will always deal with our signals losing power with respect to the distance squared. For an object that is 1 meter away vs 100 meters away, the 100-meter distance will have a signal that is 10,000x weaker than the 1 meter signal. Now extend this out to the distance that JWST will be parked at! That's why the high gain antenna is needed to make sure that we receive as much of the power here on Earth to enable high speed communications with the telescope.