A couple of hours later at about 10:10pm we went outside as instructed, and sure enough we saw a bright light moving rapidly across the night sky, underneath the moon. We'd been told that we might see both the ISS and the Space X capsule, but we only saw one moving object, so can't be sure which one this was!
As for the significance of the event, it was the first manned US flight since the Shuttle programme had been shut down almost a decade ago, and so a pretty big moment, and hopefully no more having to (rather embarrassingly for a 'superpower') as for a lift on other people's rockets.