Complex sentence: A finite impulse response (FIR) filter is a type of a signal processing filter whose impulse response (or response to any finite length input) is of "finite" duration, because it settles to zero in finite time.
Split into simpler sentences: A finite impulse response (FIR) filter is a type of a filter whose impulse response is of finite duration. An FIR filter's response to a finite length input is also "finite", because it settles to zero in finite time.