Generically: An active bass has a built-in preamp to amplify the signal from the pickup(s) and uses either an on-board battery or an external power supply to power the preamp. It outputs a hotter signal to your amplifier. It is able to boost as well as cut frequency ranges and almost always has two or three frequency controls (bass + treble OR bass + mid + treble). A passive bass uses only the magnet/coil assembly of the pickup(s) to produce a signal. It usually (but not always) has only frequency control - usually treble - and can only cut that frequency. Technically: Many "active" instruments with on-board preamps have the same pickups as do "passive" instruments. REAL active pickups (Like those made by EMG) have smaller magnets, generate less background noise than passive pickups and need the power from the preamps in order to function properly. See this link: http://www.tunemybass.com/bass_guitar_buying_guide/bass_pickups_1.html for more info.
The only electronics in a passive bass are possibly, pots, a cap, switch and jack apart from the pickps. Active means there's powered electronics in there as well. In terms of signal level, depending on the design they can be all over the place.
Active is a bass typically with a powered pre-amp onboard (9 - 18V) or outboard in some rare cases. They may be two or three band pre's that allow for a wider variety of tone from the bass. Passive is what we're accustomed to seeing in the original Fender products. No pre-amp, just magnetic pick-ups and the potentiometers (pots) and a jack for the cable to the amp. Active basses usually put out a hotter signal to the amp as well, thus the active or passive jacks/switches seen on many amps.
One of the big differences is that an active preamp on a bass buffers the output signal and can lower output impedance of the instrument permitting it to drive longer cables without upper frequency loss than can be run with a straight high impedance passive instrument.
Also, one is COOL and the other isn't!!! But I'm not saying which is which!!! Seriously, you should try both, and see which suits you. There are many reasonably priced active basses on the market, and of course, some inexpensive Fenders, or Waterstones (my brand!!). I wouldn't spend a lot of money in either direction until you are sure which approach you like more. Some folks like the band-width (if that is the correct terminology) of active basses, while others believe passive electronics are warmer and more pure.
Sorry to insert myself in this tread, but I'd like to know ''officially'' why active - passive terms are used. In bass, OK : Pickup - powered preamp - Active Pickup - volume and tone controls - passive In PA Mixer - crossover - amp - speaker - active Mixer - amp - crossover - speaker - passive. Is it because the crossover is powered in the active kit, and unpowered in the passive kit.
In both cases the element in question is powered if active and not powered if passive, notice that active basses have an onboard battery or are phantom powered and an active crossover has a power cord. Basically in a bass, passive processing can only attenuate or cut signals while active processing can boost or cut signal. Typically, passive crossovers are contained inside a speaker cabinet and are hard set to specific frequencies. Active crossovers allow the user to select what frequencies are to be split (and can boost the level if needed).