Can you describe more in detail what it is and which is its scope?
Built In Test Equipment is part of a system that monitors the correct functioning of that system. It produces an alert if part of the system fails to fulfil its function.
An example would be a system with two sets of memory chips; the BITE would copy all data to set 1, then test memory set 2 by writing and reading various test patterns. If the read pattern is different than pattern written, there is a memory error. If so, an alert is raised. If not, all data is copied to set 2, and set 1 will be tested. This is procedure is repeated at specific intervals.
Another example would be a watchdog timer which triggers a signal if a timer runs out. If the system is working correctly, it will reset the timer before it runs out. The signal from the watchdog can then for example reset the hardware, take some corrective action or raise an alert.