He was rehearsing a scene when he fired a "prop gun" (i.e. a real gun with blanks) at several individuals.
movieweb.com
Most news headlines state that it was the gun that killed the individuals, not Alec Baldwin.
Here's a tweet that he shared a few years ago.
Perhaps God is calling him to repentance...
A shooting on the New Mexico set of the Alec Baldwin movie Rust left one person dead and another in critical condition Thursday.
At 1:50 p.m. MST, Santa Fe County Sheriff's deputies responded to a 911 call that someone had been shot where the movie was filming at Santa Fe's Bonanza Creek Ranch. According to a news release, investigators reported that two individuals were shot when a prop firearm was discharged. As of late Thursday, they were still working to determine exactly what happened.
A 42-year woman was taken by helicopter to University of New Mexico Hospital, where she later died. (Deadline reported that she was a member of the crew.) A male victim, also 42, took an ambulance to Christus St. Vincent Regional Medical Center, where he is receiving emergency treatment.
Rust is described on IMDb as a Western, the story of a 13-year-old boy in 1880's Kansas who, charged with protecting himself and his little brother after the death of their parents, "goes on the run with his long estranged grandfather after he's sentenced to hang for the accidental killing of a local rancher."

Alec Baldwin Discharged Prop Gun That Killed Cinematographer, Injured Director on Movie Set
Cinematographer Halyna Hutchins is dead and director Joel Souza is critically injured after an accidental shooting on the set of Rust.

Here's a tweet that he shared a few years ago.
Perhaps God is calling him to repentance...