It is a pity the long link is causing some folks problems because the pictures there are quite helpful. The main thing they lack is motion, since it is much easier to figure out how a diff works, whether bevel or spur. when you can see the bits going around, preferably while twiddling the shafts yourself.
One way to look at it is that it is a form of analog adding device. If the road wheels are regarded as the input, then the rotations of the drive shaft are proportional to the sum of the rotations of the drive wheels. (The ratio of the crown wheel will decide what the proportion is.) Mr Babbage was planning to use this in his differential engine, among other things.
So considering it more the normal way, when the drive shaft is turned, the two driven shafts will turn so that the sum of their rotations is proportional to the input rotations. If one wheel is fixed the other will rotate at twice the speed. This is the classic problem when one wheel is in the mud and the other on the tarmac.
The Lego people make, or used to, a differential for some of the Lego Technics kits. This is a bevel type, but only has one bevel gear on the spider, which does help to see what is going on. (The input drive is a spur gear.) When one of my sons was about 11 or 12, he had been shown how a differential worked, so he built a spur gear differential out of the Lego parts that we had. It was a bit cumbersome but it really worked…so as a reward he got bought the Lego technics car, the big one with moving “pistons” and all. He is working as a programer for Google now.
regards
John