It would imply that you suddenly got up to speak to the parents or that it was important that you mention you were standing. The information "stood" is not necessary in ordinary speech unless you want to emphasize that standing was important. In Danish it is a typical fixed phrase as a way of expressing a continuing action without the use of the English gerund, which Danish does not have.
OK, it turns out the problem I've been having is that they never really bothered teaching the english language while I was in school.
If this page is correct: https://learnenglish.britishcouncil.org/grammar/beginner-to-pre-intermediate/past-continuous-and-past-simple ...then it suggests that these continuous actions only make sense to use in some contexts.
e.g. if someone says: "Hvad gjorte du klokken otte i går?" (is that how you say "What did you do at eight o'clock yesterday"?) In that case I might respond "Jeg stod og talte med dine forældre"- because that's something that happened to be happening at the time.
If I was just commenting in general I'd instead say "Jeg talte med dine forældre" because without any additional context (e.g. the time it was happening or some other thing happening in the middle of it) the continuous action is unnecessary?