At the end of the second series the mystery of the murders in Hinamizawa and the repeating time ends but that isn't the end for the characters.
The first episode of this five part OVA series is pure fan service with the characters heading to the local swimming pool. For reasons explained in the story everybody is determined to take Keiichi's swimming trunks... understandable he is equally determined that they don't.
Then we get to the three part 'Die Killing' arc... the children are cycling down a hill when Rika has an accident. She wakes up in the clinic but everything has changed. She is in another Hinamizawa where the various calamities never occurred and everybody's lives are going well. Hanyu isn't here but Rika manages to communicate with her and learns she is in a fragment universe... there is a possibility that she will be able to return to her own universe but she will have to decide quickly and do something rather drastic.
The final episode somebody breaks a magical seal in the shrine causing two items known as 'magatama' to drop from the sky. One is red, the other white; the person who possesses the red one will immediately fall in love with the person who has the white one. The red one falls into Rena's open mouth and she swallows it! This inevitably leads to trouble as the white one passes from one person to another. If they are to resolve the problem the possessors of each one must go to the shrine and a ceremony must be performed.
This was a fun third series. The opening episode was pretty silly but quite fun. The 'Die Killing' arc was better though; it opened with a shock before introducing us to a new Hinamizawa. This was done in a way that kept the viewer wondering what was happening; only learning as Rika discovers. It was fun to see the different character dynamics in this world. The final section was a fun story what provided laughs without descending into fan-service. Overall this was a good addition to the series which I expect fans will enjoy.
These comments are based on watching the series in Japanese with English subtitles.