Okay, to put it in very simple terms:
Passive means that there are pickups, wires, pots (knobs), a capacitor (a small electronic component...don't worry about it) and a jack. That's all.
Active means that instead of the plain pot/capacitor/wire setup of a passive bass, there is a preamp built into the bass. A preamp does two things: It boosts the overall signal put out by your pickups (which is very small) and it allows more radical alteration of tone. You may have noticed that passive basses generally just have a tone control, while active basses have more knobs...i.e. a 3-band EQ (bass, mid, treble).
A preamp is more or less like the front end of your bass amp...the part with the knobs. That, too, is a preamp, which feeds a power amp (a head is a pre+power amp in one box...you may have noticed that some bass rigs have separate preamps and power amps). So if you've already got a preamp in your bass rig, why do you need an on-board preamp, you ask? Well, you don't...though you may like the sound you can get from it a lot more than the sound you get out of the same amp with a passive bass. It's all personal preference.
A preamp, since it is an amplifier, requires power. That's where the battery comes in. Yes, it's a 9V. Some basses have two 9V batteries, for 18V total. If there isn't a separate battery compartment on the back of the bass, it means that the battery is under the electronic cavity cover.
Batteries should last a LONG time in normal use, but make SURE you don't leave your bass plugged in (meaning don't leave the cord plugged into the bass itself) or it'll drain in a hurry...plugging in is what turns the amp on.
Some people like the sound of passive basses, others prefer active basses.
The quality of preamps varies widely. Just because a bass is active doesn't mean the electronics are any good (it's just like stereos...a cheap a$$ stereo you buy at Wal-Mart does the same thing as a high-end audiophile system, but there's no way it'll sound as good). The high-end pickup manufacturers all make good preamps (e.g. Aguilar, Bartolini, etc.) that you can retrofit into your existing bass if you want to upgrade.
Note that a preamp doesn't actually have to be built into the bass. You can get pretty much the same thing by buying an outboard preamp (e.g. SansAmp Bass Driver DI, Aguilar DB924) for your passive bass.
Hope this helps...
