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In these games, when you are presented with choices which affect how the other characters view you and potentially change which route you go on, it's called a flag.
If you get one of Y's good end, you'll active the Y's good end global variable flag.
We're slowly starting to get more of these in the West, but for the most part relationship-themed games that get localized from Japan are still largely of the variety, where a heterosexual male protagonist pursues relationships with one (or, occasionally, more than one) of the impossibly attractive female cast members.
Oddly enough, it's Western developers rather than localization teams who seem to be leading the charge for gradually changing thanks to titles like the excellent Sweet Fuse.
This terminology is quite common even outside of visual novels in anime.
For instance, the manga The World God Only Knows (a parody of the dating sim genre of games) uses the term frequently, and the manga chapters are numbered as flags (e.g "flag 53").