FIR filters are non-recursive. That is, there is no feedback involved. Any given signal sample running through an FIR filter will have a finite number of operations performed on it (multiplications and summations) and that's it. An IIR filter is recursive. There *is* feedback involved. A particular sample from a signal will have multiplications and summations performed, but some operated version of that sample will remain in the IIR filter "system" forever (infinity) -- forever effecting the outcome of the filter to one degree or another. The impulse response of an FIR filter will eventually reach zero. The impulse response of an IIR filter may very well keep "ringing" ad-infinitum. IIR filters may be designed to accurately simulate "classical" analog filter responses. FIR filters, in general, cannot do this. Hope this helps.