@markyy -Tan is the way little kids pronounce the suffix “chan”, which in turn is the suffix you append to something in Japan to make it a “cute” something. So the adorable, kid-like aphilotus would be aphi-chan, or as aphichan himself would pronounce his name, aphi-tan!
The OS-tans, then, are Small, Cute, usually female, Childlike Anthropomorphizations of the various Operating Systems that exist. The Windows-tans are all siblings, obviously, and the Unix/Linux-tans are like a big crazy clan of incest, and the Mac/OSX-tans tend to be catgirls (thanks to the longstanding Apple policy of naming their products after types of big-cat.
OS-tans are an interesting crossover between the anime/manga sphere and the computer-geek sphere, not unlike the Alternate History Geek and Manga Geek crossover Hetalia:Axis Powers, a comic about the anthropomorphized European nations from Between the Great Wars, centering around “Useless Italy”, a smart but slightly cowardly young man, and his travails working for Germany, who is trying to train him, but always has to meet the demands of his “Crazy boss” (Hitler).
I don’t know why I know that.