Someone else on the forum dug up the patent Ford got on it which was enlightening as it showed all the various inputs to the software control of the hydraulic clutch. Which lets the system do really fun things, like look at the vehicle speed and steering wheel input, calculate the required half shaft speed differential (to accommodate the turning radius), and then ensure each half shaft is rotating at the correct speed. Note that one of the inputs in the patent is road surface, which is why it's actually important to take the time to set the drive mode correctly.
Note further that this is very different than the F-150 as shown in the video Mr. Sticker posted. The locking differential in the F-150 is an open differential with a pin to lock the gears together; it's open or it's locked. The Expedition is open, locked, or anything in between. This is also very different than the limited slip differentials in the Gen 3 Expeditions (and the current GM products) in that those are mechanical limited slip where the amount of allowable slip (rotational speed difference between the half axles) is set by the mechanical design. The eLSD is able to vary the allowable speed difference between the half axles. And, yes, the pin type design in the F-150 is a bit stronger and won't overheat when pushed while off-roading. But it's pretty useless when your wife needs to go pick the kids up from school in a snow storm. The Expedition lets you dig deeply into the operation of the system if you're going to be pushing it off-road OR toss the keys to your wife (or teenager) and tell them to just put it into "snow" mode.
from page 210 of my 2018 owner's manual:
LIMITED SLIP DIFFERENTIAL (IF EQUIPPED)
The Electronic Limited Slip Differential (eLSD) system directs torque, enabling the vehicle to drive over terrain and road conditions that a conventional axle cannot. The system is active at all times and requires no input from the driver.
Note: If your vehicle is not at optimal operating conditions or a system fault is present, a warning may be displayed in the instrument cluster. Depending on the warning, your vehicle may need to be serviced. For more information regarding the system information messages, See Information Messages (page 123)....
Trailer Towing
The Electronic Limited Slip Differential enhances vehicle stability during trailer tow operation.