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Normally, this refers to OBD-II, a federally mandated method to access information on internally detected faults and to do tests via a connector (normally SAE standard J-1962 16 pins in a trapezoidal block).
The most common visible effect of this is the "Check Engine" Light (aka MIL light) which turns on when some internal test fails and a diagnostic code is set which can be recalled (and the light turned off) using a scan tool.
Wikipedia has an article on the topic: http://en.wikipedia.org/wiki/On_Board_Diagnostics
Note that the connector often provides both information and the ability to control (given the proper interface) even outside the standard diagnostic modes, e.g. vehicle speed and RPM are normally present on the bus. As another example, OnStar uses the air-bag triggered bit to automatically detect an emergency condition.
There are various stand-alone and computer based "scan tools" able to access OBD-II systems.
The OBD=II system only specifies some required request-response methods, but can be implemented over CAN (Controller Area Network), J-1850 (SAE standard, two flavors), or other in-vehicle intermodule bus.
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