Generally speaking, the term means that there is a battery in the bass. Most commonly, the battery is being used to power a preamp. The preamp uses a battery and thus the instrument is powered (active). Occasionally, the pickups are active; a bass with active pickups would, of course, also be considered active.
Most pickups (even in ‘active basses’) are actually passive. A bass can have an active preamp with passive pickups: This is the most common scenario.
EMG, MEC and some others have models that are active and require a battery. Sometimes these pickups are used with preamps as well, but not necessarily.
Many preamp manufacturers are designing their control harnesses with passive pickups in mind, as they are more common both as retrofit parts and for OEM use.
Systems with active/passive switching
Some instruments have a switch which changes the signal from active to passive.
This switch is not changing the pickups, or how they function: the switch is not making a pickup active or passive. It is changing the signal path for the controls.
More precisely, an active passive switch is a bypass switch. When in ‘passive’ mode, the signal bypasses the active part of the preamp (which is typically the EQ section).