I'm seeing more evidence that there is not widespread "immunity" to COVID-19, but that there is a large group of people who have better immune system responses due to exposure to other types of coronaviruses (i.e. common cold, etc).
One was a guy in Hong Kong (I think) which is the first confirmed reinfection. By DNA sequencing they see that he was infected with a strain that had a very slight DNA difference to his first infection. His first infection was symptomatic; his second was not.
With that and some other reports there is a suggestion that if you have T cells and B cells that have experience with other coronavirus types that have a similar structure, that it makes your body much more able to quickly recognize and fight the infection before it spreads to the extent it would in someone who does not have that T cell or B cell "memory". And thus it can better explain the extremely wide variation in outcomes, from people who are completely asymptomatic to people who become gravely ill.
I haven't seen this final part anywhere, but this could also explain part of why it doesn't seem to hit kids hard. As we all know, kids are walking petri dishes of germs,, so perhaps the fact that their immune systems are so exposed to and used to fighting off common colds contributes to them having better outcomes from this virus?
I can say from personal history, I used to NEVER get sick. Then my eldest son went to preschool, and for 6 months I got EVERYTHING. And then I stopped getting sick. My wife works in a Dr's office, and when she first started, she was sick constantly. After a few months, that went away. But then when she met my kids and eventually moved in, she got EVERYTHING they had as well for a few months, and then it went away and now she's fine.
I'm sure it's not that suddenly my kids became more hygienic... I think it's that our immune systems have seen so many germs that they make a quicker attack on new germs coming at us so we're still "getting" infected but it remains asymptomatic based on immune system response. If something similar happens here, perhaps that's helping to blunt the impact of this thing.