Hello again Itix :)
A passive, or mechanical, centre diff is for example a "normal" LSD diff which relies on real time speed differences between the shafts on each side of the clutch plates to generate friction to get the diff to lock.
In a diff like this you adjust the locking mainly by the number and type of friction plates, and ramp angle (on throttle and off throttle.) A steeper ramp angle will generate a higher treshold for the diff to lock, and vica verca.
On an active diff the locking of the diff is not relied on real time shaft speed differences, but by sensor generated input. So you can program the diff to lock/open when you want, no matter differences in shaft speed etc.
In its simples form it would kind of be like programmable ramp angles and preload.
If you take a "simple" road car active diff system like the electronically opperated BMW Xdrive, you could theoretically send all power too one wheel (three active diffs, front, centre and rear). That system is working with electroniv servo motors opening and closing the clutch plates.
A rally active diff works in much the same way, but by using hydraulics instead of electronics to do the locking/opening.
(Edit: BMW Xdrive might not be the best example according to Mirek)
(BTW, its open for any engineer/expert to correct me if Im wrong.)
Edit 1: Added "preload" to the programmable example.