Recently, Zack Snyder sat down to watch the extended cut of Batman v Superman: Dawn of Justice and invited online audiences to watch alongside him as he provided commentary on various parts of the movie that he himself directed. Among other topics, Synder also revealed the reasoning behind why Superman was killed off in his second movie.
Zack Snyder revealed that the scream Superman emitted when he was stabbed by Doomsday was an important plot point, and a set up for the next film in the planned series, Justice League. The sound of the scream is what was supposed to have awakened the Mother Boxes and alerted Steppenwolf. This plot point would have received a callback in Justice League, whose trailer carried a scene where Steppenwolf remarks 'No Kryptonians'.
Aside from setting up the conflict in the next movie, Superman's death was also supposed to serve a symbolic purpose. The movie begins and ends with deaths. Bruce's parents die at the beginning of the film, and their demise leads him down the dark path that eventually leads him to ruthlessly take the lives of criminals.
With the death of Superman at the end, Batman's allowed himself to turn away from the dark path and begin healing himself. This was exemplified in the scene at the end where Batman chooses to not brand Lex while he was in prison. And the same healing applies to the rest of humanity, as they finally come to the realization that the Superman they doubted and feared was ready to sacrifice himself on their behalf.
In short, Superman's death set him up as the embodiment of hope for Batman and the rest of the world, while also setting up the circumstances that would prompt Batman to arrange for his resurrection in the next film to deal with Steppenwolf.
The commentary shows the amount of forethought that Snyder put into his five-movie plan for the DCEU, but also highlights his greatest weakness as a filmmaker: his insistence on dealing with grand ideas and mythic archetypes at the expense of creating actual three-dimensional characters.
One of the biggest complaints that critics and fans alike had with Batman V Superman was the scant time given to showing what Superman thinks of what is happening around him. His actions are always reactive, and rarely proactive. Batman brings the fight to Superman. Lex brings the fight to both heroes. Even Wonder Woman is on her own mission. Superman, on the other hand, only shows up when someone is in danger or when he is summoned by the Bat-signal or the sight of Lois Lane in mortal danger yet again.
As a result, we get very little idea of who Clark is as a person, and so there is little impact of his death on the audience, especially since the shot of the dirt rising on top of his coffin near the end of the film let everyone know his death was going to be a temporary inconvenience rather than a permanent consequence that would carry some weight. This news comes from The Hollywood Reporter.