Concerned citizens around the Neon District would inform Cole about other citizens being abducted from the streets by gangs of Reapers and would ask him to free them. Each of these citizens would then point out where the abductions were taking place. Cole would then face each group of Reapers, defeating them one by one to free the captives.
Note that you will gain experience points for each citizen that survives. It can prove quite useful to defeat the Reapers with headshots using Precision if possible. Taking them out quickly in this manner can reduce the chance of any of the hostages getting accidentally harmed or killed, as there will sometimes be an RPG-weilding Reaper that could end up harming the civilians when firing its rocket at you. Also note that these missions gradually become more difficult, the later ones having Reaper Conduits among them.