HDMI has always been intended for External connection to HDTV's where as a Display Port is a interface for connecting flat panel display on computer systems.
a DP (Display port) was predominantly designed for modern flat panel displays and chipsets. DP has a micro-packet architecture with low voltage signal that work better with networked displays. it also allows daisy chaining of multiple displays with full graphics performance without utilising any GPU channels.. this includes 3d and content protection.
where as HDMI is based on legacy CRT raster-scan architecture and will use a single channel of the GPU. it is able to transmit audio and data so is ideal for HDTV's.
DVI is similar in architecture to HDMI except it cannot transmit audio, but is still able to support 120hz at 1080p.
newer gaming monitors are usually offering DVI, HDMI and DP as a input. usually the HDMI connection is there only if the monitor has speakers to utilise the audio path on HDMI cables.
hope this helps.