A PDF stores text as positioned characters on a page, not as paragraphs — there's no concept of 'this is one sentence' baked into the format. Converting to Word means reading every character's position, grouping the ones that sit on the same line, and grouping lines into paragraphs based on the gaps between them, then writing that back out in the .docx format Word understands.
That works well for the documents most people convert — letters, reports, contracts — where the layout is basically one column of text. It works less well for brochures, forms and multi-column pages, which is why the FAQ above is upfront about the limits rather than promising a pixel-perfect copy.
Everything runs in your browser. Your file is never uploaded, never queued on a server, and never deleted from one — because it was never there.