I understand that this thread originated due to the debate about MLD, BLD, LSD etc getting too technical in another thread.

The thread is filled with jargons and technical terms to the level that a layman will find it hard to understand, so let me try to translate a bit :
What is a differential and why was it invented ?
When the non-steered rear wheels of an RWD vehicle are subjected to a turn, say a right turn, there has to be a mechanism to allow the inner wheel to turn at a lesser rpm than the outer wheel, so that when the vehicle changes it's orientation gradually from straight to 'right turned' , no tyre rubber 'screeches' against the road or 'slips' against the road and gets shaved off.
Turns out, the mechanism is 'already there', because the rubber that forms the tyre, needs to 'twist' at the contact patch, when wheels which have no steering have to 'turn'. Utilizing this fact, a basic 'differential' (called open differential) was invented, with a system of rotating cogs that works in the following way :
A way where the 'energy' gets split equally amongst both wheels - the inner rear wheel experiences more tyre rubber twisting load on it's contact patch than the outer wheel, because it's trying to achieve a sharper change in orientation due to smaller turning radius => more torque demand presented by inner wheel w.r.t outer wheel => the ratio of rpms between wheels is inversely proportional to the ratio of torque loads between the wheels. Effectively torque x rpm (the energy/sec) on each wheel is the same, and this is a neat mechanism.
However, all hell breaks loose (the energy getting split equally goes out the window), when there is very poor or no friction on offer, on one of the wheels amongst this left and right. The design of the open differential is such that the 'engine torque' that needs to be generated is defined (through gear ratio translations of course) purely by the smaller of the two torques demanded by the left and right wheels. This aspect creates an issue. When one wheel is on a slippery surface (sand or ice) the 'load torque' on that wheel is effectively the rotational inertial mass of the wheel+tyre+brakedisc
of that wheel alone. That means even if the 'other' wheel is sitting on a proper grippy surface, the torque-demand or torque-load presented to the engine is that of the slipping wheel, which is low. The engine will only generate as much torque as is presented as load to it (previous post above).
So now, there is one wheel with grip, and the open differential is ineffective in 'utilizing' it. In other words, the open differential is something that allows the flow of energy through the path of least resistance.
To combat this problem, the question now is, 'how to present a higher torque demand to the engine, when one of the wheel is simply slipping and presenting none'. Thus was invented things like MLD, BLD, LSD etc. (all jargons, but with careful meaning hidden in them - mechanically locking, brake locking, limited slip). All of these are trying to build a relationship between the left and right wheels, something that the open differential never allows. These jargons are trying to 'counter' the fundamental edict behind the invention of the open differential - FROM "let the load dictate how much torque demand needs to be presented to the engine" TO "let us artifically remove the independence of the left and right loads from each other and then present a 'cooked up' torque demand to the engine".
In case of MLD, the left and right are simply locked into a single solid axle, the left and right have to rotate at the same speed. In case of LSD, there are clutch packs present, that can control the 'resistance to turning' offered by left side or right side. In case of BLD, the brake computer (or ABS computer) externally uses it's brain, to actually press the brake discs to 'artificially' create extra torque load wherever necessary.
In case of open diff, the effective torque demand to engine is the smaller of the two "contact patch friction load" required to rotate the individual wheels.
In case of locked diff (MLD), the effective torque demand to engine is the larger of the two "contact patch friction load" required to rotate the individual wheels.
In case of a slipping diff (LSD/BLD), the effective torque demand is the smaller of (contact patch friction load + brakes pressed load) required to rotate the individual wheels.
Hope this is useful to a layman reader.