a crossover is a knob on an amplifier designed to power component (individual) drivers
your home theater receiver is made to power full-range speakers, which have what's known as a passive crossover inside the box.
A crossover sets the limit to the range of frequencies you want a given speaker to play.
A subsonic filter is the same thing, but limits how LOW you want your subwoofer to play. A sealed enclosure, for instance, is essentially tuned at 0hz, so no subsonic filter is necessary. A ported (has a hole in it) enclosure is tuned to a specified frequency (usually as low as 20hz for SQ setups, or as high as 60-80Hz for SPL competition setups) and playing frequencies lower than the tuning frequency of the port can damage the subwoofer, regardless of the amount of power being used.
A subwoofer rated to take 2000 watts RMS, for instance, could easily be destroyed by playing something as small as 500w through it, and not using a subsonic filter