Unlike most other online tuners, this is built on new WebRTC technology. What does that mean for you? Previously tuner's have required the use of flash, which is becoming an outdated technology and requires plugins for your browser.
WebRTC is not yet supported on any of the iOS browsers. Until that time I recommend any of the free guitar tuner apps out there, including my own
First check that you've allowed microphone access on your browser. This is usually displayed at the top of the screen. You must also make sure that your microphone volume is loud enough.