running active is a term used for components that are hooked to a power supply and usually have settings that can be changed. remember, crossovers are not only used for audio, but for video, rf propagation, radar, and all sorts of other applications. active and passive systems are used throughout many types of electronics.
for example, passive crossovers in an audio system do not require external power, and they have fixed attenuation of frequency. they are put inline to a speaker (or speakers) and may have jumpers on them to change some settings - they way that works is by having multiple crossovers on one board, with a physical connector the installer moves to select the proper crossover. a benefit of the passive crossover, is that it enables the user to disect the bandwidth on the input side to several smaller portions on the output side. so one channel of amplification can drive multiple speakers.
an active system has to be powered, weather by a battery, or a power supply. there are usually digital or analog dials, knobs, or settings to adjust what the unit is made for. example, the active crossover in an audio system will allow you to adjust a low pass filter for chanel 1 between 1000hz and 5000hz. the drawback, is that each speaker or group of speakers need its own channel of amplification after the active processing. the settings are dependant on the unit and its engineers.
other examples of active versus passive are inline GPS amplifiers, antennas, etc. the main point is that active requires outboard power, and passive utilizes the power already present in the signal path.
i hope that helps
