How your infrastructure looks like? С program on one computer, browser - on another? Do you have any web-server?

There are a lot of different ways.

1. You can write web-server in your С program and open it in browser.
2. You can send (with a lot of protocols - http API, snmp, syslog, raw udp, etc) data from С program to WEB server, save there and show in browser.
3. If you have everything on one computer, you can also make web server with your С program, or make the page in files with js that uses websocket to communicate. Then you will need to use websockets on С side.
4. The easiest way - save data to file and use html page with js which will parse local file every n seconds.