LoL Duel now runs on the web. For security, browsers don't let a website read the game client on your computer directly. This small app is the bridge: it reads data from the client, hands it to the site, and writes the rune page the site computed back to the client. The site works fully without it — you just pick your champion and opponent by hand.
The bridge listens only on your own machine (127.0.0.1) and can't be reached from outside. Only allowed site addresses get a response, and writing runes requires the pairing key — a site in another tab can't write to your client.