A "data broker" is any company that collects personal information and sells or displays access to it, without you ever handing it to them directly. Most of what they have comes from public records (property deeds, voter rolls, court filings), marketing and survey data, app permissions, and each other — brokers buy and resell data between themselves constantly, which is part of why removing yourself from one doesn't clear the others.
People-search sites (Whitepages, Spokeo, BeenVerified, and most of the sites in our directory) show a name-searchable public profile, often free with ads or a paid "full report." Data brokers proper (Acxiom and similar) don't have a public search page at all — they sell data in bulk to advertisers, and getting off their list usually means a direct opt-out request rather than finding and deleting a listing.
Brokers refresh their databases from the same public-record and marketing-data pipelines on a schedule — weeks to months, depending on the site. Opting out removes today's listing, not tomorrow's. That's the actual case for a paid service: not that the manual process is hard (it isn't, mostly — see any page in the directory), but that doing it again every few months, across a hundred-plus sites, doesn't stay done on its own.