An Air-Gap refers to the physical separation of an electronic device such as a computer from all networks. A device may be vulnerable to intrusion or spying, but in theory, this is a logical "low-tech solution to a high-tech problem" which prevents all spying and attack attempts.
Problems with an air-gap
The obvious problem is that while "they" cannot access the potentially vulnerable device, that device also cannot access other harmless servers and resources on the Internet or LAN. Only off-line activity is possible. However, even an air-gapped device can be monitored. Delayed reporting strategies can be used, such as having spyware record activity which may be physically retrieved at a later time. Another such strategy would be loading logs onto the user's external device, such as a flash drive, and retrieving it from that device once it is connected to a networked computer.
Other strategies which would not use spyware include either attaching monitoring hardware directly to the device, or even recording electromagnetic emissions from a computer keyboard. This can be dome over some distance, and although it can prove difficult to separate out from ambient interference, can be used effectively to determine the binary output of the keyboard. These binary signals can then be translated into the letters they represent.