The goal of a servo controlled subwoofer is to more accurately control the speaker itself for more accurate bass reproduction. In theory, this could use an internal (active) or external (passive) setup, but I believe the amplifier needs to be built around the concept of the speaker being servo-controlled and handle it correctly.
http://www.rythmikaudio.com/DirectServo.html
Active subwoofer: Has the amplifier built in.
Passive subwoofer: Requires an external amplifier.
Good servo subs sound phenomenal, and often have a matching price. ($$$$$)
But, most subwoofers are active. They have an amp built into them. This is 'traditional' subwoofer design and makes sense as the amplifier can be matched to the speaker that is inside of it exactly. Most A/V receivers do not have amplification built in for a woofer, and so in almost all cases you MUST use some sort of external amplifier to power the speaker. That amp can be built into the subwoofer box, or not. Since it's easiest to build it in and sell it that way, that's most common. That way, the wiring is also consistent to a subwoofer. Just a coaxial cable to carry the signal from an A/V receiver to the subwoofer.
Some VERY entry level home theater in a box kits use non-standard setups. They have a powered subwoofer output that runs directly to a non-powered woofer box. This is convenient for them, but it may make a subwoofer upgrade problematic.
If you are looking for a good subwoofer, come up with a budget and ask specifically about the best sounding subs at or near that price point. Be aware that subwoofers generally sound better and hit harder with greater accuracy with the more money that is spent. I swear by sealed subwoofer enclosures with pretty significant price tags. Every time I listen to a cheaper model I often find them boomy. There's a reason the reputable brands have $1,500+ subwoofers out there. Highly respected value brands still end up with those pricey models for a reason.