A passive use capacitors, and sometimes inductors and are wired in line with your speakers after the amp..meaning it provides no electrical current hence being passive.
Active uses circuits among other things and is before the amplifier putting out at least as much voltage as the was put into it. Both have their pros and cons but realistically they do the same job..but a crappy active can introduce noise to the system so it just depends on what you want it to do.
Mike