Some people stand during kiddush and some sit. Some stand for Friday night kiddush and sit for Shabbat lunch. Sometimes there is a moment of confusion and of awkward standing up and sitting down when you are a guest at someone's house and don't know their custom.
Some rabbis infer from the talmudic rule that we must say kiddush as part of a meal that there is a requirement to sit, as you would at a meal, during its recitation. Based on this, sitting for Shabbat morning kiddush is a common custom. On Friday night, however, most people stand.
The Mishnah Berurah explains that the reason for standing is that Shabbat evening kiddush is a form of testimony and in Jewish law, witnesses must stand. Kiddush at night is part of fulfilling the obligation to "remember the Shabbat" (Exodus 20:8). In kiddush, we recount the Shabbat of Creation and God's resting on the Seventh Day.