The "right to be forgotten" is the popular name for the right to erasure set out in Article 17 of the UK GDPR. Although Brexit ended the UK's membership of the EU, the General Data Protection Regulation was retained as UK law in 2021, so the right still applies in essentially the same form. In practical terms it means that, in certain circumstances, you can ask a search engine, a website, or any other organisation that holds your personal data to remove it.
For most people in the UK, the right to be forgotten matters in one specific context: getting a search engine like Google or Bing to stop returning a particular page when someone searches for your name. That process is technically called "delisting" and it does not delete the source page - only the link in the search results. Understanding that distinction is the first step to using the right effectively.