Cloud Strife was born in the village of Nibelhiem. He often got into fights with the local children. At the age of fourteen he becomes enamored with stories of Sephiorth and SOLDIER. He travels to Midgar to join SOLDIER. However he fails the application process and is rejected. Disgraced but unwilling to return to Nibelhiem he joins the army and becomes a Shinra MP, basically a grunt.
Zack by contrast is a success story. Zack was born in the tropical backwater of Gongaga. He also travels to Midgar hoping to join SOLDIER and is successful. By the time CRISIS CORE begins Zack is a second class SOLDIER and is being recommended for first class by his mentor Angel Hewley. The defection of Genesis Rhapsodos from Shinra however triggers a crisis at Shinra and Zack is forced to killed his mentor during a mission at Modeohiem. Zack and Cloud meet for the first time on this mission and bond quickly over their common history of being "backwater experts". Cloud and Zack go on to become best friends and co-workers Shinra.
Two years after Modeohiem, both Cloud and Zack are present during the Nibelhiem Incident. Sephrioth, Zack and two grunts (one of which is Cloud) are sent on a mission to check on a malfunctioning Mako reactor. After discovering the secrets of his heritage, Sephiroth goes insane and massacres Nibeliem. Zack goes to confront Sephiroth at the reactor but is defeated. Taking Sephiroth by surprise, Cloud wounds and defeats him by tossing him into the Lifestream after being impaled on his sword. Wounded, both Cloud and Zack are captured by Hojo are experimented on underneath the Nibelhiem Manor.
Four years later, Zack escapes from Nibelhiem dragging Cloud along with him. Cloud has contracted Mako poisoning from the experiments and is comatose. Zack spends the next ten months on the run, hunted by both Shinra and Genesis. Zack finally is confronted by the Shinra army near Midgar and is gunned down shortly before Cloud regains consciousness. Cloud takes Zacks sword and travels to Midgar, beginning Final Fantasy VII.
In contrast to the rest of the FFVII timeline, Cloud's time at Shinra is poorly defined except for a few key moments. This is a boon to writers who can fill in on what canon leaves out. This seems to be a pattern with the Zack/Cloud paring since the two years at Shinra, the four underneath Nibelhiem and the ten months on the run all leave a lot to the imagination and are not filled in at all except for some moments. The lack of clarification even attracts many het authors to try to expand on their relationship.
As a ship, Clack shares some similarities with Sefikura, the more well known and arguably the most popular FFVII slash ship, however Cloud's and Zack's relationship is never antagonistic in canon, unlike Cloud and Sephiroth. Despite not being one of the less well-known ships in the FFVII fandom, Clack is not a crack ship and has a created over the years a large backlog of fanfictions that can be found if one is willing to look.
It is one of the less well known slash ships among the fandom and yet among one of the oldest, and has existed in some form since the release of Final Fantasy VII back in 1997. In the original game Zack is a minor character who died before the story began. His story has since been expanded upon in the various prequels since.