Back in 1993, Superman died while fighting Doomsday. In the comics, the world mourned the death of the Man of Steel, and soon saw other Supermen rise to take his place. The real Superman eventually returned to life, and his adventures continued. That was in the previous comic continuity. In the current continuity, which started in 2011, Superman is dying again. This time, his death and return is something different.
Superman has had a tough time lately. His secret identity was exposed to the world, he started to lose his powers, discovered his cells had mutated so he could no longer absorb sunlight, and had to use Kryptonite to destroy the mutated cells. His powers returned, to a degree, but now he had Kryptonite poisoning, which was killing him. If all that wasn't bad enough, a new threat arrived, and Superman used his solar blast to counter his foe's blast to take him out.
Superman was able to say his final goodbyes to his loved ones before his body disintegrated. He had already accepted that the Kryptonite poisoning was killing him so this final sacrifice was something he did without a second thought. As the energy within was expelled (and you'll notice some hit Lois Lane and Lana Lang), Superman died.
Strangely enough, there is another Superman in the world. When the DC Universe was rebooted in 2011 and became known as The New 52, the previous comic universe changed. The heroes were younger and didn't have all the experiences and relationships they had before. It turned out the Superman from the pre-New 52 continuity survived as a result of a crossover story called Convergence. This Superman was still married to Lois and had a son they called Jon. They lived, in secret, in the New 52 Universe.
The existence of this older Superman was revealed to the New 52 version during this last battle. He was later approached by a mysterious figure calling himself Mr. Oz who told him, "You and your family are not what you believe you are, and neither was the fallen Superman." With the revelation that Wally West from the old continuity was still alive, this brings into question how there could be two different Supermen? Mr. Oz's world could mean that the New 52 Superman wasn't actually the real Superman and the older version is actually the true one. This is a concern for a later day.
The fallen Superman was buried and honored, but the older version knew death wasn't necessarily the end for a Kryptonian. When he was killed by Doomsday, his body was revived in a Kryptonian regeneration matrix. With the help of Lana Lang, he took the remains of the fallen Superman to this world's Fortress of Solitude. Unfortunately, this Fortress did not contain a regeneration matrix.
The fallen Superman is dead and will remain so. The older Kal-El will honor the sacrifice and memory and reclaim the mantle of Superman.
Superman is dead, but the true Superman is back where he belongs.