An exploit is a piece of software, a chunk of data, or a sequence of commands that takes advantage of a bug, glitch or vulnerability in order to cause unintended or unanticipated behavior to occur...
An Exploit is the Thermal Exhaust Port on the Death Star
In Star Wars, the Rebel Alliance took advantage of their technical readout of the Death Star in order to find it's one weakness: a small, two-meter-wide port that could cause the whole station to explode. Only when the attach commenced did the Empire find the vulnerability, and even then they didn't consider it a threat to their massive space station.
The same is true of servers and other systems. Brilliant inddividuals with intensely intimate knowledge can launch a successful attacks on susceptible systems, even when the administrators of those systems consider them safe. This often results in the leaking of information, (credit cards, passwords, etc) or even complete annihilation of the system itself.clintandrewhall