On many systems, interrupts may be divided into three categories--not just two; many systems only support two of the three, but there may be some difference as to which two they support.
An edge-triggered interrupt will cause the CPU to switch to interrupt mode any time interrupts are enabled, the interrupt line has been in the inactive state some time after the interrupt was last reset, and has been in the active state some time after that.
A "pure" level-triggered interrupt will cause the CPU to switch to interrupt mode any time interrupts are enabled and the interrupting signal is currently active.
A "pure" level-triggered interrupt will cause the CPU to switch to interrupt mode any time interrupts are enabled and the interrupting signal has been in its active state since it was last reset (if it was in its active state when reset, it may have simply stayed in that state).
A major advantage of level-triggered interrupts is that if while a device is being serviced for one reason, another reason emerges that would cause it to require attention (or another device using the same line requires attention), the CPU will keep revisitng the device until it is completely satisfied and has no cause to hold the reset line.
The primary disadvantages of level-triggered interrupts are that they often require that the CPU take explicit action to reset them (edge-triggered interrupts are often implicitly reset by the interrupt controller when the interrupt is dispatched), and that an interrupt which gets enabled when the CPU has no idea how to service it can lock up the system, since the CPU will do nothing except repeatedly invoke the interrupt handler because the device will continuously need (but never receive) attention.