Their purpose was to steal the trilithium resin, an extremely unstable byproduct of warp travel that accumulated in the ship's engines. Her plan was foiled by Jean-Luc Picard who had briefly returned to the ship to get his saddle for he had heard from Calvin Hutchinson that there were horses on Arkaria.
Kelsey was killed when the trilithium she was transporting to her starship exploded. Picard had removed the dynamic stabilizer that had kept its container from vibrating and triggering the material. (TNG: "Starship Mine")