Any kind of spread inversion, whether it's the 3mo-30Y or 2Y-10Y is simple in principle: you will get paid more for shorter duration bonds compared to longer duration bonds. This is opposite to what normally happens, hence the term inversion.
Shorter maturity (<<10Y) bonds react more to Fed policy. Longer maturity (>=10Y) reflect long-term expectations of growth/inflation.
So if the shorter maturity yield is higher than the longer maturity yield, the bond market believes that near-term federal funds rate will be higher higher than future growth/inflation.
This means the bond market believes the rate hikes are high enough that a slowdown will occur requiring rate cuts.
Because there are many different bond durations (1 month to 30 years), you can have many different bond pairs that can be inverted or not. This is often displayed on a yield curve.
An alternative way to display this is to show the individual yields plotted on a single chart. Normal behaviour is when the yields increase with duration (i.e. whitest line at the bottom, reddest on the top). Inversion is when any shorter term yield line goes above a longer term yield line.
You can pan this chart around to see what happened in previous crashes and compare it to the current situation.