The purpose of this is to ensure that organizations like the European equivalents of RIAA and MPAA have basically one click disable buttons (not strictly required, but how most sites will implement it) for content they claim infringes their copyrights, or is otherwise illegal. This would also be used by organizations that track down child porn etc.

As for who is a trusted flagger: "The status of trusted flaggers under this Regulation shall be awarded, upon application by any entities, by the Digital Services Coordinator of the Member State in which the applicant is established where the applicant has demonstrated to meet all of the following conditions: (a) it has particular expertise and competence for the purposes of detecting, identifying and notifying illegal content; (b) it represents collective interests and is independent from any online platform; (c) it carries out its activities for the purposes of submitting notices in a timely, diligent and objective manner. "

I.E. if you can convince your local government that you should be one, bam you are one, and online platform the EU needs to expedite processing of any notices you make.

On the other end of the spectrum, the companies are required to allow you to appeal takedowns and account suspensions/terminations (for TOS or illegal content reasons, not for non-payment reasons) for a 6 month period. Further, if you appeal a takedown or account suspension and the company rejects your appeal, the law will allow you to take the matter to binding arbitration. If the user wins, the company pays all costs, and must reinstate the content or account. If the user loses, they only pay their portion of arbitration costs. (The company's portion are just part of doing business in the EU).