The Death of Nagisa Okazaki is when she gives birth to Ushio Okazaki and dies shortly afterwards. This happens in episode 16 of Clannad After Story This happens at the beginning of 2006 in the anime and 24 December 2006 in the visual novel.
In the winter, Nagisa goes into labor two weeks early. Soon, Akio and Sanae arrive. As time passes, Tomoya states that Nagisa continuously passed out due to pain and eventually, gives birth to Ushio. Nagisa immediately slips away. Tomoya tries to keep her awake, but Nagisa is unable to hold on and dies. When Tomoya realizes this, he hugs Nagisa's corpse and recalls memories of their time.
For five years, Ushio lived with Akio and Sanae. Tomoya resorted to alcohol and smoking in this time.
At the end of the Ep 8 Valiant Fight of Clannad: After Story Yukine Miyazawa talks about the town's famous folklore which says,"Whenever something good happens or someone achieves true happiness an orb of light appears in the sky. If you find one, it'll grant you a wish". In Ep 19 The Road Home, when Tomoya Okazaki sends his father back to his hometown an orb of light appears in the sky and slowly goes into Tomoya's body which grants him a wish.
After Ushio (and maybe Tomoya) die, Tomoya wishes for them to stay alive. He is sent back to the place where Nagisa and Tomoya first met. At first, he resents meeting her, but he can't live without her. Therefore, he shouts her name and meets her. Then, they are brought to when Nagisa would have died, but Nagisa miraculously survives and they live happily.