Dodgy app developers make dodgy apps, and convince naive users to install them.
The dodgy apps make the naive user's Internet connection available to some partner the dodgy app developer has done a deal with - and since the naive user is typically using a residential network, and it lets their connection be used by someone else, it's called a residential proxy.
The partner sells access to a huge network of residential proxies to scrapers, often those wanting to do AI scraping against the wishes of the owners of the site being scraped. This is valuable to the scrapers because they appear to be coming from large numbers of different residential addresses. Cloud / hosting provider addresses are usually the first thing people block if they don't want scrapers, and they also block how much each address can access. So the scrapers scrape a little bit per address, making it hard for the victim sites to detect what is scraping and what is legitimate traffic.
This creates a security risk for the naive users, because as well as connecting out to the Internet, usually the proxy customer can connect to and maybe exploit things on their home network. The naive users usually don't know their connection is being used this way.
So the headline here is that one of the affected naive users is someone in the White House, and one of the 'residential' networks being sold is in fact the White House's Internet connection.