Ten inch active speakers are self-powered pro audio speakers that have a ten inch woofer for low frequency reproduction, and a built-in power amplifier module. These speakers do NOT need any external power amplifier, as the amplifier module is built right into the speaker enclosure itself.
To use a ten inch active speaker you need to run a power cable to it, and you need to run a signal cable to it from your pro audio mixer. The signal cable is ordinary, everyday 3 pin XLR microphone cable, so you don't need anything special or exotic to hook them up.
Ten inch active speakers are best used for vocal sound reinforcement in situations such as meetings, auctions, or just for general announcements. They are very handy for playing music at wedding ceremonies, but if you are going to crank them up for the dancing afterwards, you probably need to add a powered subwoofer.