Basic virtual reality browser based solutions have existed since the 90’s (e.g.browsers which supported VRML, the Virtual Reality Modelling Language that allowed you to create 3D interactive worlds). The graphics quality was quite… 90’s, but it was the starting point and was great for its time.
WebVR has advanced to a point that it allows you to browse the web the classic way (pc or mobile screen with mouse/keyboard/touch input for navigation) or virtually (with a head mounted display (e.g. Google Cardboard, Oculus Rift, Samsung Gear VR) that uses motion sensing technology or classic technologies for input (mouse, keyboard)) and does not require the use of any plugins.
Mozilla and Google are the major players in enabling WebVR through the Firefox and Chrome browsers.
WebVR is work-in-progress and still needs more time to mature. If you’re using a recent version of Chrome or Firefox check out some of the WebVR demos on http://mozvr.com/ and http://webglvr.tumblr.com/