What PDF metadata reveals
Besides the pages, a PDF carries document information: a title, the author's name, a subject, keywords, the program that created it, the PDF producer and the creation and modification dates. Viewers show the title in the window bar, search engines may show it in results and document systems sort files by it.
It can also reveal more than you want. The author field often holds the full name from the computer account, the creator shows the exact software, and the dates show when a document was really written. Checking this before sending a CV, a contract or an offer takes a few seconds.
Two places, both handled
PDFs store metadata in two places: the classic information dictionary and an XMP block that many newer apps read first. Changing only one of them leads to the old title still showing in some viewers. When you save, the tool writes your values to the information dictionary and rewrites the XMP block with the same values. If the file is marked as PDF/A, that mark is kept.
Removing metadata for real
Remove all metadata deletes the information dictionary, every XMP block in the file (including those attached to pages and images) and private data that apps like Illustrator store. Many tools only unlink this data and leave it inside the file, where it can still be read. Here the file is rebuilt and anything no longer used is left out, so the old values are not in the bytes. To clean many files at once, use Remove PDF metadata.