Q: I still don’t get how the yield curve inversion works, or why it matters.

A: Last week, we mentioned that an inverted yield curve is often used to predict recessions. Just the same, an inverted curve is not a guarantee of recession. It means that short term interest rates are higher than long-term interest rates. In other words, you are getting paid more for short-term savings than for long-term savings, which is usually an indication of future economic weakness. For example, the rates for CDs are currently higher for shorter durations. If there is a continued belief that interest rates will be lower in the future, maybe in response to a recession or other economic weakness, the inversion will persist.
There are some aspects to the current economy that make the yield curve inversion a little harder to assess. Brad McMillan explains what this means for a potential recession, after providing a very helpful explanation:

If these predictions pan out—and, so far, they are consistent with the data—then we can draw two conclusions. First, a recession is unlikely for the next several quarters. Second, we likely will not get one unless the Fed does keep hiking.
This is good news for us as investors. Right now, earnings are projected to keep increasing this year. And if we don’t get a recession? That increase is more likely. Second, valuations depend on interest rates. Even if the Fed keeps hiking, that may well push longer-term rates down, providing more support for markets.