You can connect a mobile device (a phone or a tablet) with a TV directly over a built-in TV wifi, however if the TV is older, but it already has an HDMI port, you can use HDMI dongle as ChromCast, which was introduced by Google or one of the similar devices with similar functionalities as Miracast, or Mirascreen, EzCast or AnyCast. With all these devices you need to install an app to your Android or iOS device. If you are looking for devices like this check our category: connecting the phone TV connection.
Wi-Fi can be used also as an HDMI extender, which can replace a long HDMI cable for example over 10m long. In this case the HDMI signal is firstly converted into wireless wi-fi signal, which is received by a wi-fi receiver and then transfered back to high quality digital HDMI signal. You may check also our category HDMI extenders.