1. Switching from analog VGA technology to the digital HDMI allows the transmission of a much larger amount of information. Higher resolutions like full HD (1920x1080) and even WQXGA (2560×1600) can now be achieved. The quality of the video being transmitted is also considerably better.
2. Recent versions of the HDMI standard now allow high quality 3D to be transmitted natively. This enables your computer's graphics card or your Blu-Ray player to send 3D video to your HDMI monitor exactly how the producer intended it to be, without being converted from 2D to 3D or using inferior cardboard 3D glasses on a standard monitor.
3. HDMI includes many other advanced technologies such as CEC (Consumer Electronics Control) to allow your HDMI monitor to be controlled by other devices and making it possible to have a single remote control for several devices. Ethernet and audio can also be carried along with the video signal. Having audio support has several benefits, such as giving you flexibility in how you connect your audio equipment. If your HDMI monitor has built-in speakers, only one cable is required to connect both your video and sound.
If you want to have the latest and greatest technology, or are upgrading from an older VGA monitor, I highly recommend choosing a monitor that has HDMI available.