Curiously my girlfriend (who has no interest in sci-fi particularly or technology) really got into Star Trek very quickly. Think I happened to be watching early Season 2 and she enjoyed it so we ended up watching the whole run. Then the whole of DS9. Then the whole of Battlestar Galactica remake. She enjoys shows that are character driven which ST has in barrel loads so not hard to see why she enjoys it. The sci-fi/alien edge just makes it more interesting.