JavaScript was the first programing language that runs in a browser. Historically this was the main reason, JS was developed for the most used browser in 1995: Netscape. Also this implementation become an standard: ECMAScript. Be the first, the most used and became a well-defined standard are requisites to success.

Microsoft tried to do their own language for browsers called JScript (based in JavaScript but really incompatible with the ECMAScript specification). JScript was important but the people preferred the compatibility between browsers and not the features on JScript, so they supported more the JavaScript implementation.

With this scenario, JavaScript become the unique supported programing language in the browsers. Other companies tried to create the next generation of browser-languages like Google with Dart but JavaScript is so expanded that it's practically impossible to be substituted in short-term.