C680 FO reported the aircraft brakes were mistakenly released due to a communication problem with the Captain and the jet began to roll when the chokes were removed.

Narrative

Aircraft rolled forward upon captain removing chocks. Parking brake was not set.Preparing for repo from Jet Aviation to Atlantic at KHOU; I performed power on including setting parking brake and then PIC and I together completed cockpit prep. We got up and down from seats a few times and at one point PIC asked me if parking brake was set and I said yes and then he said remove it" by which he meant to remove chocks but I didn't understand and asked him if he wanted me to release parking brake and he said yes so I did that. A bit later I was in seat and PIC was up and he asked me if I had removed chocks and I said no; so he went down and removed chocks. My head was down programming box and I heard him yell; 'stop!' Or something like that and I looked up to see us rolling forward and line tech giving signal to apply brakes. I selected aux hyd pump on and rested brakes to stop; then set the parking brake. Luckily nobody was injured and no impact occurred or was close; but with slower reaction there certainly would have been an impact with aircraft parked in front and to our right."