I'm an absolute layman, but "no worse than the common cold" doesn't sound too great to me since I've always been told you can keep getting the cold over and over again. What am I missing?
If you look at the Wikipedia article, you will find more detailed information, but the common cold is caused primarily by rhinoviruses. However, some are also coronaviruses and even influenza viruses. There are hundreds of viruses that cause "the cold."
Here's my understanding (also a layman but trying to read as much as possible):
A new coronavirus jumps from an animal to humans. No human body has seen this type of virus before, so when it infects the immune system has to work a lot to learn how to fight it. This causes symptoms like a fever which is a sign of the ongoing struggle. For frail people it means the immune system is not strong enough to counteract the infection and it spreads and potentially kills them.
However, if the immune system learns quickly enough how to fight it, antibodies are killing the virus faster than it can multiply and you get better. The antibodies then disappear in a few months but the long term memory cells remain.
Later, the virus infects you again. You develop the symptoms of a light respiratory infection but the immune system quickly references the memory cells and is able to produce suitable antibodies really fast. The fight is short and easy, the antibodies defeat the virus before it has time to spread. There is no sign of the struggle like first time (no fever) but only the light symptoms we don't even think of (common cold).
Now, how about children? Well as we see already they're unlikely to be seriously affected (low mortality). And children get lots of fevers (parents can confirm). So probably sometimes in the early years we get infected by some coronaviruses our bodies have never seen, the immune system puts up an intense fight and builds the long-term immunity that will be with us as adults.
There are several coronaviruses that cause what's commonly known as "the cold". If you catch one and recover you're likely to be immune against infections from the same viral strain for some time.
For SARS-CoV2 and the COVID-19 disease it causes this means that even without the - quite likely - availability of a vaccine over time natural immunity will build up within individuals and the population as a whole, which has the potential of both making the resulting disease less severe and future waves spreading less.
If most individuals who contract the virus during the next few months can't get sick anymore and can't spread the virus anymore for the about 6 months those individuals are taken out of the equation, which leaves less individuals for the virus to spread to in the next wave.
