Convert PDF to PDF/A — Convert a PDF towards PDF/A for archiving, embedding fonts so the document renders the same years from now.
Flatten a PDF — Flatten a PDF so form fields, annotations and signatures become part of the page and can no longer be edited.
Questions
What actually makes a PDF large?
Almost always the images. A scanned page is a photograph, often stored far larger than anyone needs. Recompressing those pictures is usually where the entire saving comes from.