In Serenity (2005), A woman carrying a bucket and her son are looking at the trading station a few buildings away:
Son: I'm telling you I heard it. Repeater.
Woman: Did sound somewhat like gun blast. Maybe you ought run tell Lawman.
What does "Repeater" mean?
A "repeater" is a term for a repeating firearm.
A repeating firearm or repeater is any firearm (either a handgun or long gun) that is capable of being fired repeatedly before having to manually reload new ammunition into the weapon.
The term was used pretty heavily around the era that westerns tend to cover, so the use of it in Firefly is likely an homage to how the show is basically a space western.
The son is referring to the sound of Jayne's automatic weapon being fired.
Jayne fired thirteen rounds of ammunition into the tunnel that Captain Reynolds had just opened. The woman and her son heard it.
"Repeater," the boy said, referring to Jayne's gun. River had never heard it called that — Jayne just called it "Phoebe."
"Did sound summat like gunblast," the woman with the bucket said. "Maybe you aught run tell lawman."
We see these being referred to as "repeater" weapons elsewhere in the franchise;
The cattle rustlers drew to a halt in front of the house. Ottoline Beavertail herself was at the forefront, astride a noble-looking palomino with a coat like spun gold. She held a repeater rifle one-handed with the butt wedged against her hip, barrel pointing to the sky.
