The ship may be full of DHARMA crew being transported between projects.
"Antonius" is the Latin origin of the name Antony, as in Marcus Antonius (="Mark Antony"). Antonius is therefore the name of an important Roman political dynasty. Mark Antony claimed that his family originated with a son of Hercules called Anton, i.e., that they were descendants of an immortal bloodline.
"Helgus" possibly derives from German and Scandanavian words for "holy."
The name "Helgus Antonius" alludes to the notion of a powerful family which views itself, perhaps falsely, as descended from a special ("holy" or even immortal) ancestry.
The name refers to the notion that the Widmore family, who may have built the ship in collaboration with the Hanso Foundation, constitute a powerful dynasty, descended from a "great" man as alluded to by Charles Widmore during his interview with Desmond.
The name refers to the Hanso dynasty, and Alvar or Magnus Hanso as a great man deemed "holy" or "immortal."
The map snapped by Rachel Blake supposedly showing the destination of the Helgus Antonius is in fact a map of the Island. It shows a lake in the north, similar to the lake in the barracks where the Galaga submarine is moored.
The Helgus Antonius is en route to the island, retracing the last known route of Magnus Hanso's Black Rock.