It's a pass mark from the ABP Köln. As to what that means...
During WWII, Germany had regional offices that processed mail going to and from foreign destinations. There were known as Auslandbriefprüfstellen (ABP), or foreign letter examination offices. The ABP were under the command of the Oberkommando der Wehrmacht (German Army High Command), foreign countries and intelligence division.
There were eight offices, each with a letter designator:
a — Königsberg
b — Berlin
c — Köln (Cologne)
d — München (Munich)
e — Frankfurt
f — Hamburg
g — Wien (Vienna)
h — Hof
These offices were responsible for conducting any censor examinations. Mail that was opened for examination would be resealed and have a censor mark (Prüfstempel) and typically an individual censor ID mark (Prüferstempel) applied. Mail that was not opened would receive what was called a Durchlaufstempel, or pass mark.
As your item is a postcard, there was no need to open it for examination, so only a pass mark was applied. The "A.c" identifies the mark as coming from APB (the "A") Köln (the "c"). These marks could be applied by either a handstamp or a machine. Yours is the machine mark.
It's listed in Landsmann's
Die Zensur von Zivilpost in Deutschland im 2. Weltkrieg (The Censorship of Civil Post in Germany in WWII) as CDM1.1. Rarity grade is "B", meaning common.
