Darker than Black: Gaiden is seen as a 3rd season by a lot of people and they have plenty of reason to think that since it came out after the 2nd season. If you’ve watched Darker than Black, these OVAs are essential in the storyline, they aren’t your typical OVAs of recent vintage which are mostly hot springs and beach episodes.
These 4 episodes fill in the giant gaping plot hole gap between seasons 1 and 2. Season 2 seems almost as if it’s a different timeline without these 4 episodes. Any questions that were left unanswered with that 2nd season are answered here. The story revolves around Hei and Yin exclusively. They have left Tokyo and are on the run from the Syndicate and others. In these OVAs, you get to learn more about Hei and Yin and their relationship with each other while their on the run from the groups after them.
I would say that in terms of production, these OVAs are the best of the bunch but that is probably because it was the last in the chain. It came out after the 2nd season even though the story is from before that season. The sound, the music and everything else are probably the best of the series.
Without this set of OVAs, the 2 seasons feel disjointed and almost like they’re 2 different shows. If you plan to watch Darker than Black for the first time or 27th time, the OVAs are a necessity. It would have been perfect if these came out before the 2nd season did instead of after. So it should be Darker than Black: Kuro no Keiyakusha, the OVAs and then Darker than Black: Gemini of the Meteor.