As you climb you look for faults in the rock (cracks usually), Into these you place devices intended to jam into place and no pull out. The two best known devices are nuts and cams. Nuts are shaped in a special way to hold them in place and cams have a trigger mechanism that you operate to close the cams on the end of the devices while you insert them. When you let go of the trigger they expand and grip. Both of these are attached to a wire loop into which you insert a carabiner and then you insert your rope into that. The end of the rope is tied into your harness and the other end is controlled by your second who has you on belay using a braking device. The second feeds you the rope as you need it through the braking device and if you fall locks the device and hold you on the rope. The idea is that if you come off the rock you only fall twice the distance from your last piece of protection (the distance to the the protection and the same again past it.
A controlled fall is when you realise that you're in trouble and are likely to take a fall and sort of push yourself off instead. You shout a warning to your second who immediately puts you on full brake and braces for impact. The second is usually on a piece of rack that can be stood on and is tied to the rock face by two protective devices as a minimum.
Not a lot of use in everyday life though lol