A PDF page's content and its visible boundary are two different things — the content can extend past the edge that gets displayed or printed, which is exactly how bleed and crop marks work in professional printing. Cropping here moves that visible boundary to wherever you drag it, using the same mechanism a print shop's crop marks would use.
The preview you drag against is a real render of the page, produced the same way a PDF viewer draws it, so what you select is what you get. Because it's a boundary change rather than a re-render of the page itself, cropping doesn't touch the text or images — everything stays exactly as sharp as it was, just framed differently.
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.