The DJIA is the only common stock index composed of stocks that have been carefully chosen to represent the range of industries that make up the economy. Most other indexes are composed of stocks chosen using relatively simple algorithms: the S&P 500 is the top 500 US public companies by market capitalization, the NASDAQ Composite Index is all companies that trade on the NASDAQ exchange.
The 30 companies in the Dow Jones, on the other hand, have been chosen to be most representative of their respective industries. And the composition of this group is changed over time to reflect how important various industries are in the US economy.
While there's some subjectivity to this selection, and even possibly some form of self-fulfilling prophecy (adding a company to the DJIA may attract investors to it), historically the DJIA has correlated pretty well with the market as a whole. And it can be easier to understand why it moves as it does, because there are so few variables involved.
It can be instructive to look at how the composition of the Dow 30 has changed. The current index is heavy in information tehnology (Apple, Microsoft, IBM, Intel, Salesforce, Cisco), financial services (Visa, Goldman Sachs, JPMorgan Chase, AmEx), health care, and retailing (although the retail sector is still all brick&mortar chains -- it can't be too long before Amazon.com joins). Many years go there was a much larger emphasis on industrial machinery and agriculture because those were much more important sectors of the US economy. General Electric was in the index since its inception (over a century), but was replaced in 2018 as they had been struggling to find their place in the 21st century economy, even though they're still an enormous company.