(covers information from several alternate timelines)
A home was a "place of residence. Social unit formed by a family living together." (TNG: "The Offspring", "Reunion", "New Ground", "The Masterpiece Society") Home also represented "the safe and the familiar." (TNG: "Journey's End") A home could range from one's house to one's homeworld. The term "homesick" referred to one's desire to return home or their own people. (DS9: "The Die is Cast"; VOY: "Fury")
When Lieutenant Commander Data became acquainted with the Iconian language in 2365, he was able to confirm Captain Jean-Luc Picard's hypothesis that it was the parent tongue of a language family that consisted of Iccobar, Dewan and Dinasian. He was able to construct "a basic working understanding through a comparison of common root words such as 'mother', 'father', 'child', 'home', 'tribe', 'food', 'life', 'death', yours, ours, mine..." (TNG: "Contagion")
Later that year, when Q wished to join the crew of the USS Enterprise -D, he gave the reasoning that "this ship is already home for the indigent, the unwanted, the unworthy. Why not for a homeless entity." (TNG: "Q Who")
When Data first brought his daughter, Lal, to his quarters for the first time in 2366, he explained to her that they were "home" and were together a "family". (TNG: "The Offspring")
During a visit to Ten Forward by Sergey and Helena Rozhenko in 2368, they were greeted by Guinan, who observed them looking out the window. She noted that "You know, sooner or later, everyone comes in here. They stand by those windows and they look out and the stare. They're looking for that little star they call home. It doesn't matter how far away it is, everybody looks anyway." After some time talking, and discussing the matter of Worf and his discommendation, Guinan comforted them, revealing that there was the part of Worf that cherished them, and when he "looks out the window towards home. He's not looking toward the Klingon Empire. He's looking toward you." (TNG: "Family")
Following the return of Montgomery Scott to the Enterprise-D in 2369, after being rescued from the USS Jenolen, Scott visited the holodeck where he sat on a recreation of the bridge of the original USS Enterprise. While there, he was visited by Captain Picard, where they discussed the past. When Scott admitted that he felt in the way in the future, he explained of the Enterprise, "This was my home. This is where I had a purpose." (TNG: "Relics")
When Tom Paris discovered Kes viewing a course back to Ocampa while aboard a Class 2 shuttle in an alternate 2371, he inquired if she was homesick. Surprised by Paris' arrival, Tom told her "it's okay, a lot of people on board feel the same way." When Kes attempted to deny her desire to return home, she said "I spent my entire life trying to get away from Ocampa. Why would I want to go back?" Paris replied simply "because it's home," before explaining to her that "home for me means a penal colony. Out here, I get to fly a state of the art ship, and there's no admirals in sight." (VOY: "Fury")
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