It used to be that Web browsing was simple. You asked a server for some text, which was duly sent, and then formatted by your browser. Now a web page is as likely to be a full-blown application that is reading mail, editing text, or lots of other things and may use WebSockets to create a back channel to the server. Thanks to affordable hardware like the ESP8266 one of those things a modern web browser can do is sense and control the real world. [Acrobotic] has an interesting video about using WebSockets to allow a browser to talk to an ESP8266 web server in real time. You can see his simple demo in the video below.
Of course, you’ll use the usual language you use on the ESP8266 — [Acrobotic] uses C++ in the Arduino IDE. On the browser side you’ll use JavaScript, although that will be embedded in your C++ program which acts as a web server.