When you open this tool, your browser simply displays an HTML file stored on your computer. Think of your browser as a universal file viewer. Just like it can show PDFs without Adobe or images without Photoshop, it displays this HTML file without needing any special software.
The "verification" part uses the Web Crypto API, which is built into every modern browser. This is essentially your computer's calculator doing math with your file's data. The calculation happens entirely within your browser window, which is called "client-side" processing. Your file never leaves your computer, and nothing gets saved or uploaded anywhere.
Think of it like using Windows Calculator to add numbers. You type 5 + 3, get 8, and nothing is sent online. Hash verification works the same way. Your browser reads your file, does the math, and shows you the result. All local, all offline, all safe.