In the Half-Life universe, transportation portals through space (and time?) are a reality. Whether it’s shot by a handheld device or free-floating in space, these portals are wormholes to different locations. In Portal, they simply moved you from place to place. In Half-Life, they also between different places, but both here on Earth and on the borderworld.
To go to and from Xen requires satellite communication, at least, as far as I know. They use these portals to go to Xen for extraterrestrial research. Gordon Freeman was just some schmo who tested an extraterrestrial crystal which made the portal between Earth and Xen (and possibly some currently unnamed world) become unstable, bringing forth all sorts unforeseen consequences.
Black Mesa (the research facility, not the mod) is funded by the United States government for various unanswered reasons, but probably military. When the link between Earth and the alien worlds via Xen became unstable, the HECU was called, and, well…