A ghost hack is the process of hacking someone's reality by attacking and taking control of their cybernetic implants. The term comes from Masamune Shirow's manga Ghost in the Shell, where a ghost means the soul or spirit of a being, while it's shell is just the nice wrapper that the ghost happens to be living in, the meat (or the cyborg body or the glass tank or that supercomputer sitting in the corner). When someone has been ghost hacked, their consciousness is subservient to the commands of whoever hacked them. The really scary part is that the target doesn't know it; they think they are in control of their actions, but are actually just someone's tool.
The primary effect of the ghost hack is that people think things that are simply not true. Of course, people do this all the time right now, but it is currently rare for someone to believe that they are married and have a daughter when they are actually a bachelor. Shirow calls these simulated experiences; you remember it all, but none of it really happened.
Likely due to the fact that Ghost in the Shell is, plotwise, a political drama, people who have been ghost hacked tend to end up being used as unwitting spies or assassins. Given past real projects, such as MKULTRA, it seems likely that intelligence agencies of the future will attempt such activities as soon as it is feasible.
In Stand Alone Complex, they add a neat new wrinkle to this, letting very skilled ghost hackers, such as Kusanagi and The Laughing Man, perform real time hacks; usually ghost hacking someone takes hours but they can do it in seconds. The Laughing Man uses this a lot to make himself invisible without the aid of thermoptic camouflage; while this would be ineffective against someone without a wetware implant, a basic rule in Ghost in the Shell is that nearly everyone has such implants; they are as necessary to people in 2029 as a driver's license is to people living in a suburb today. Kusanagi and Bateau both use this ability to great effect by causing visual hallucinations to distract and confuse enemies. They can make someone think that they have been killed, or simply create an illusion showing themselves in one place when they're actually on the other side of the room.
The idea of a ghost hack goes to the core of the real issues in Ghost in the Shell. If you commit a murder while ghost hacked, are you responsible for your actions? You literally had no choice in the matter, but nonetheless it was you who pulled the trigger. In Ghost in the Shell, there is mention that when people commit crimes, there is an investigation to see if they themselves committed the crime, or if a malfunction or malicious attack caused it. However, given that a skilled cracker might be able to evade detection, ghost hacking someone gives you the ability to commit a crime and get away without a trace, letting them take the fall.