All 360's have at least one video port, there's the standard "A/V" port that all consoles have and there is an HDMI port on newer models in addition to the A/V port.
The A/V port is a multi-format port that uses a proprietary main plug that has pins for just about anything. This single connector contains composite, component, S-video, VGA, analog (L/R) audio, and digital (optical) audio. It also has a few pins that manage "cable detect", a VGA cable will wire the pin that tells the 360 to output VGA signals while the HDAV cable wires both the SD and HD wires to a switch on the plug so that it can operate as either an SD cable or an HD cable.
The HDMI port is a standard HDMI (1.2?) port that uses a generic HDMI cable. It outputs an HD digital picture as well as digital audio. It can be used with an HDMI-DVI cable to function as a DVI output as well, but this means that the audio signal is lost as DVI devices can't decode it. To compensate, Microsoft made an audio cable that plugs into the A/V port and has analog (L/R) and digital (optical) audio outputs. This means you can hook up a screen with HDMI and still use an optical cable to connect a receiver.
The same can be done by modifying a normal A/V cable. To make both plugs fit, the case from the A/V cable's plug must be removed, making the plug slimmer. If you take a cheap VGA cable (not VGA-VGA, Xbox 360 A/V to VGA) and cut off the case from the A/V end, you can fit it with HDMI at the same time. These Xbox VGA cables also have optical and analog audio outputs on them which can be used instead of the HDMI's sound.