A great deal. Every 3-dB decrease in loudspeaker sensitivity requires a doubling of amplifier power to achieve the same loudness. That's why you should match the receiver's output power to your speakers' sensitivity. If you need more than 170Wpc, either because you have insensitive speakers, a large room, or like to play soundtracks quite loudly, you'll need a separate digital controller and power amplifier rather than a receiver. With a subwoofer in the system, low bass frequencies are filtered from the signals driving the main loudspeakers, which reduces the amount of amplifier power needed to drive them.
Low bass requires more amplifier power to reproduce than do midrange and treble frequencies.
By directing the bass to the subwoofer and away from the main speakers, the receiver's power amplifiers don't have to work as hard. Adding a powered subwoofer reduces the receiver's power-output requirements by about 20 percent. Features A-V receivers vary greatly in their features. These connectors allow you to tap into the low-level signals before they are amplified by the receiver's internal power amplifiers, and connect them to a separate power amplifier. In essence, you're replacing the receiver's internal amplifiers with more powerful external ones.