I'm not an expert, but here's my take. I think the general answer is that pickups aren't necessarily 'active', the electronics in the guitar are either passive or active, and pickups are designed to work with either an active or passive circuitry. Bill is right in that Alembic pickups, being low impedance, need an on-board preamp, i.e. active electronics, whereas high impedance pickups don't. In either case the pickups themselves aren't 'active'; the term 'active' refers to the presence of a preamp in the instrument and a power source for the preamp circuitry. I think there may be some pickups that have a preamp built in to the shell rather than separately installed in the instrument. There's a good wiki on the subject
here. Some manufacturers call their pickups active pickups, but again, technically, I think this refers to the fact that they are designed to be used with a powered on-board preamp, i.e. active electronics. That's my understanding, but I'm not an expert.