Flame arrestor
Could be terminology used causing confusion.
If you are talking afterburner jet engines used on fighter planes the more common terminolgy that I have seen is "flame holder"
At any rate what they are used for is to keep the hottest part of the flame inside the engine where it can raise the energy /pressure of the gas before a duct area change (nozzle) that changes the energy into thrust.
If you didn't have a flame arrestor/holder than the air velocity within the engine woud carry the fuel droplets aft of the nozzles (either turbine inlet or afterburning) and you would continue your burning too far aft to be of use (nice blowtorch effects but quite inefficient)
The flame arrestor/holder is designed to create local turbulence which in turn increases residence time of the fuel within a given engine area so that you complete combustion of the fuel spray where it was intended.
well that's a start, let's see what else folks can add