A DMCA takedown is a formal notice asking a website, hosting provider, or search engine to remove or disable access to content that infringes your copyright. Under the Digital Millennium Copyright Act, service providers that act promptly on valid notices keep their "safe harbour" protection from liability, which is why most of them take notices seriously.
A valid notice identifies your original work and the specific infringing URLs, gives your contact details, includes a good-faith statement that the use isn't authorised, includes a statement under penalty of perjury that the information is accurate and that you're the owner or authorised to act for them, and is signed. It goes to the provider's designated copyright agent or abuse contact. Effective enforcement doesn't stop at the site operator: when a site ignores notices, filing with its hosting provider and with search engines usually gets better results.
Privly files DMCA takedowns as a registered US Copyright Office DMCA designated agent, so notices are signed by Privly as your authorised agent and your legal name stays off them. Privly also escalates to hosts when sites don't respond and tracks notices through to removal.