My humble, layman's understanding of active inceptors relates to the video game consoles we have at home in our living room. When something exciting happens, in addition to audio and visual feedback, the controller vibrates.
In the avionics world, active inceptors are used to diminish excitement, not enhance it. They provide tactile feedback to pilots who need to keep their eyes looking out of the cockpit, not down at instruments.
The most common use of active inceptors is to remind a pilot when he is reaching some kind of an important limit. At the threshold, the stick may vibrate. If the pilot continues past that threshold, the stick may actively resist. The pilot can push through, but the message is 'be sure you know what you're doing here'. Typical parameters reinforced by resistance include operational or design limits of the airframe, gearbox or engine.
Since active inceptors work with electronic fly-by-wire systems and not traditional mechanical systems, they contribute to the reduction of 'aircraft complexity, maintenance requirements, life-cycle costs, and control systems volume,' and weight. They also reduce maintenance owing to the exceedance of system limits.
BAE Systems says they are the world leader in active inceptor systems. My thanks to them for talking me through this interesting subject.