Trivia: When Eric first goes back to his apartment, right after he returns from the grave, it is raining inside the apartment and his movements look an awful lot like the movements he just made in the rainy alleyway. [Not really a mistake, but worth noticing - the filmmakers were forced to re-use some shots after Brandon Lee's death.]
Trivia: In one of the flashback scenes, we see T-Bird reading from a book - "Abashed the devil stood, and felt how awful goodness is." The book is Milton's Paradise Lost. (NOTE: the line after this sounds like it is also a quote from the book, but it is not) David Patrick Kelly, who played T-Bird was so into his character that he bought an antique copy of the book. It is this we see him holding in the scene.
Trivia: Right after Gideon's Pawn Shop blows up and the police officer and Eric are talking, the officer yells at the people looting the shop; one looter is running away with a TV set. This is actually James O'Barr, creator of The Crow comic series! He was on the set one day and the filmmakers asked if he wanted to be in the movie.
Trivia: Brandon Lee, who plays Eric, suffered a fatal wound, while shooting the death scene for his character. An improperly cleaned prop gun shot a dummy tip into his stomach, which resulted in his death.
Trivia: The latter part of the scene with Eric and Albrecht in Albrecht's apartment was actually ad-libbed. Brandon decided to pick up a picture of Albrecht and his wife and ask him about it. The following part about Shelley ("Believe me, nothing is trivial") was also not in the script. The scene was originally scripted to take place in the street outside the police headquarters, but it was decided that it should be moved to Albrecht's home so that the audience could learn more about him.
Trivia: When Brandon died, there were still eight days of filming left. To finish the rest of the film, they used a body double and some digital composing. Dream Quest did the special effect for breaking the mirror, and stunt/body doubles were used when he enters the loft.
Trivia: The main crow used for filming was named "Magic." He was a trained animal used for the production of films and television. Magic also ended up being the main crow used in the production of all three sequels.
Trivia: Occasionally in the film, you may notice that Eric has a light scar going under his eye and over his nose. This is a reference to the graphic novel, in which Eric had a similar scar. Eric was shot in the head - the shot cracked the bone under his eye, creating the wound.
Trivia: Original "Crow" comic creator James O'Barr donated most of his earnings from the film because he felt it was "blood money" after the death of Brandon Lee. The only things he bought with it were a car for his mother and some speakers. The rest went to charity.
Trivia: Chad Stahelski was a close friend of Brandon Lee and was working as his stunt-double on the film. After Lee tragically died, Stahelski served as his body double for unfinished scenes. Stahelski later became famous as a film director, helming all four "John Wick" films. Due to Lee's death, he is reportedly incredibly strict on his sets when it comes to firearms safety.
Trivia: Stone Temple Pilots originally contributed a song to the film's soundtrack called "Only Dying." Following Brandon Lee's death, the song was pulled from the soundtrack and replaced with the song "Big Empty" instead.
Trivia: Aside from the tragic death of Brandon Lee, the film's production was reportedly extremely difficult. A carpenter suffered electric burns in an accident. A crew-member injured himself with a screwdriver. Another crew-member crashed his car into a studio workshop. And a grip-truck caught fire. Drug use was also rampant on-set (much to the annoyance of star Brandon Lee and director Alex Proyas, who were trying to remain professional and do their best), which may explain some of the accidents.
Trivia: The film originally had a number of scenes featuring a decomposing, zombie-like character called the "Skull Cowboy," who was played by character-actor Michael Berryman. The character would act as a sort-of "spirit guide" for Eric Draven, and do things like explain the rules of the crow to him, and offer him advice. All of his scenes were ultimately scrapped, as they were deemed unnecessary.
Trivia: Michael Massee, the actor who shot the prop gun that inadvertently killed Brandon Lee, was deeply affected by the event. He took a year off from working on any projects to simply relax and deal with his emotional state. He also reportedly refused to watch the finished film, and still hadn't seen it at the time of his unfortunate passing in 2016 from cancer.
Answer: There is no explaination given in the films, they are just brought back when the crow feels it is the right time to avenge their murder.