Why these run in your browser
A PDF holds a JPEG natively, under a filter called DCTDecode, which means a jpg to pdf conversion is not really a conversion at all. Your file is placed inside the document exactly as it is, at full quality, and the whole job is writing the few kilobytes of structure around it. That is small enough to do on your own machine, so we do.
It matters more here than on any other page of this site. The things people turn into PDFs are passports, bank statements, degree certificates and signed agreements. An ordinary online converter asks you to upload every one of those to a server you know nothing about. Nothing you drop on these pages is transmitted anywhere, and you can prove it by disconnecting from the internet after the page loads.
What these pages do not do is read an existing PDF. Opening one needs a full renderer, which is a large program we would have to load from somewhere else, and that would break the only promise worth making here.