[ALittleLight]

My really simplified explanation is:

Your inputs are lists of numbers. Your outputs are lists of numbers. There exists some possible list of numbers such that, if you multiply your inputs by that list you'll get (approximately) the outputs.

In this conception that possible set of numbers are the weights. "Training" is when you run inputs, compare to known outputs, and then update the weights so they produce outputs closet to what you want.

Large Language Models, it may be hard to see how they fit this paradigm - basically convert a sequence to a list of numbers ('aardvark' is 1, 'apple' is 2 etc) and then the desired output is the next word in the sequence (represented as a number). Surprisingly, if you get good at predicting next word in sequence you also get the ChatGPT et al behavior.