Henry was the manager and sometimes barman at Bianca's Cabaret, an exclusive nightclub that offered drinks and entertainment to clients from all over the universe.
History
Bianca and Henry set up the nightclub in the broken-down shell of Bianca's TARDIS, on a planetoid located at the nexus of a dimensional maelstrom, with wormholes connecting to many distant places in the universe. Bianca was the singer. Henry maintained the operations. His responsibilities included keeping the nightclub dimensionally stabilised and running the taxi service that carried clients through the wormholes.
Behind the scenes, both Henry and Bianca were working with separate factions of the psychic worms which inhabited the planet. Henry's allied faction, the Shadows, were beings with only a potential for existence. Henry wholeheartedly helped them take psychic possession of anyone who visited the club, giving the Shadows some semblance of physicality.
When the sixth Doctor and Iris Wildthyme showed up, they helped the factions of worms get the last pieces of knowledge they needed for their grand plans. However the Doctor stopped the plan by using his own TARDIS to time ram the club, destroying it. With the local potentialities lost, Henry, Bianca and the Shadows faded away into nothingness. (AUDIO: The Wormery)