People should care that the Dow hit 20,000 because it directly affects their investments and 401(k) and other retirement plans. In just the weeks after Trump was elected president, over $1 trillion in new wealth has been created. Don't try and tell me that people should care about that. People are becoming wealthier because the market is going up.
While '20,000' is just a number like any other, it is a number that hasn't been reached before. It shows that some individuals and corporations are making wealth, regardless of the position of anyone else. The significance of Dow hitting 20,000 is more obvious for those who are invested in the stock market, but they aren't the only ones who can gather information from it. Those who are impoverished, or have lost there jobs, or otherwise feel that the economy is in a very bad place can see the number and realize that the fact of the matter is that wealth is just not distributed evenly.
The stock market is an indicator of how well the economy is doing and how well it is expected to do. If stocks are up the economy is doing good, which means economic growth, more jobs, more money being put into the economy, etc. People should care as much about stocks being up as they do when they crash.
I think the Dow reaching 20,000 is significant because it represents about a 2,000 point increase since the November election. This Stock Market benchmark, being forward looking, indicates that many investors are expecting improved economic conditions going forward. Market goes up under Obama - historical! Proof he's doing good!
Market goes up under Trump - No big deal. Probably won't last. Not real.