Homn had ties to the Troi family as early as the 2330s. When Lwaxana Troi began destroying all evidence of Kestra, a daughter that died in childhood, he secretly saved a photograph of Kestra, which he kept hidden for the next forty years. (TNG: "Dark Page")
Homn was hired as Lwaxana's manservant prior to 2364 as a replacement for Mr. Xelo. He traveled with Lwaxana to the USS Enterprise-D in 2364 for the almost-wedding between Lwaxana's daughter, Deanna, and Wyatt Miller. (TNG: "Haven")
Homn returned with Lwaxana to the Enterprise-D in 2365 when Lwaxana was sent as an ambassador to the conference on Pacifica. He assisted Lwaxana during the trip on her ill-fated attempt to find a husband. (TNG: "Manhunt")
Homn assisted Lwaxana in her almost-wedding to Campio, the minister of Kostolain, aboard the Enterprise-D in 2368. He helped alter Lwaxana's wedding dress, which had previously been Campio's mother's, when she was to marry Campio. (TNG: "Cost of Living")
When Lwaxana fell into a coma aboard the Enterprise-D in 2370, Homn was one of the people Deanna spoke to in an effort to find out what was causing the coma. After it was discovered that the coma was part of Lwaxana's efforts to suppress the memory of her dead daughter Kestra and Lwaxana had come to terms with the accident, Homn returned the photo of Kestra he had saved to the Troi family. (TNG: "Dark Page")
Homn often joined Lwaxana on her voyages and was reported to frequently have "outrageously lustful thoughts." Given her penchant for claiming this of many people, Jean-Luc Picard included, the veracity of this assertion is questionable at best. (TNG: "Manhunt")
He had an indulgent temperament in more than one sense of the word. It could be seen in the way he patiently catered to the (sometimes exasperating) whims of his employer, as well as his quiet indulgences in the "perks" of his employment. For example, he apparently had no inhibitions in finishing off half empty glasses of wine while cleaning up dishes, and once even snacked on the very berries he was sent to pick for his employer. (TNG: "Ménage à Troi")
Appearance and habits
Homn was a tall, pale humanoid man with two fin-like ears who rarely spoke save in sign language, a skill at which he was quite adept. (TNG: "Haven") Homn possessed strength superior to that of a Human, and frequently consumed very large amounts of alcohol without experiencing any apparent effects. (TNG: "Manhunt")
The script notes from "Haven" described his first appearance, from the transporter pad, as "a gaunt figure a flowing black robe materializes. He has faded white-grey skin and beady purple eyes. He moves smoothly and deliberately. Quite a ghostly figure this Mr. Homn."
"hom" was the pronunciation of this character's name from the script pronunciation guide for "Manhunt". 
Neither his species nor his homeworld have been revealed. His position and demeanor (but not his appearance) are very similar to that of a Hupyrian, the members of which species are also highly prized in the galaxy as manservants and who only speak to their employers.
Homn appears in the Star Trek: Deep Space Nine comics "Lwaxana Troi and the Wedding of Doom" and "Four Funerals and a Wedding", where he accompanies Lwaxana to Deep Space 9 so Lwaxana can marry a Bolian called Var Ulos.
In the non-canon story Triangle: Imzadi II it is revealed that, though his appearance and normal traits would insist the contrary, Mr. Homn is revealed to be rather fast, easily dodging the disruptor fire of Romulan troops.
In the non-canon story "The Ceremony of Innocence is Drowned" in the anthology Tales of the Dominion War, Mr. Homn is killed during the Battle of Betazed, shielding Lwaxana and her half-Tavnian son when the Troi household collapses under Dominion fire. Shortly before his death, Lwaxana confides to two of her Human friends that she exaggerated Homn's lustful thoughts about her.