An active or powered speaker is a speaker with the amplifier built-in.  An active speaker differs from the traditional home audio speaker in that, while it still requires a power source and some type of audio signal feed, it does not require an external amplifier/receiver or speaker wire.  A common type of active speaker that most people are familiar with is your typical Bluetooth speaker.  A rechargeable battery is the common source of power to the amplifier and an audio Bluetooth signal from a Bluetooth enabled device serves as the audio signal feed.  Another common type of active speaker that not as many people are familiar with is an active studio monitor.  Active studio monitors are typically powered by an electrical power source such as a power outlet and until recently were mainly used by musicians at concerts and in recording studios.  Because of their application, studio monitors must produce sound that is robust and accurate and in general are of higher quality than traditional home audio speakers.  Many people actually use active studio monitors and have been doing so for years.  However, until recently active studio monitors had to be physically connected to an audio source by some type of audio cable.  So it could be said that both Sonos speakers and active studio monitors are high quality active speakers, but Sonos are wifi wireless and active studio monitors are not.  Thanks to Google Chromecast Audio, however active studio monitors can be made wifi wireless and function just Sonos speakers.  Check out my other post HERE which explains in more detail how to create wifi wireless sound system that is superior to a Sonos system.