A passive speaker needs power from another source (i.e. a power amplifier). An active or powered speaker has an amplifier built in; therefore it needs a signal cable and a power cable run to it.

The advantage of an active speaker is that there is a very short run of speaker cable as the amplifier is right next to the speaker components. Long runs of speaker cable can result in both power and signal loss. The other advantage is that the manufacturer can precisely match the amplifier to the speaker.

The passive speaker has the advantage of being lighter, cheaper (you have to buy an amp to run it, though) - and more flexible, in that you may not need an amp for each speaker.