I don't get chessable

I have just looked at a very few lessons but what it tries to accomplish I don't understand. You are shown a correct move and then asked to repeat it (which anyone can do). When the variation finishes you are asked to repeat all the moves of the variation (which also anyone can do unless you have a serious short-term memory problem).

What is this process exactly meant to accomplish?

That's trying to hardwire stuff into your noggin. Like learning languages with flashcards. It's not an analysis- comprehension- application -synthesis process. As noted above, repetition is the name of the game. Any higher learning would come much later. 

I do not understand Chessable either. Good to know we are on the same page. Maybe it’s an enigma never to be solved. Like how the pyramids were built. Or how my lunch miraculously disappeared from my desk after returning from a brief trip to the bathroom. Something only to be solved by only the brightest of minds. I am too feeble-minded to give a helpful response.

Business- To take money out of your pocket!!

I understand how this repeating and imprinting in memory only work for certain things. E.g. standard positions like Philidor, Luciana, etc. Maybe forcing opening lines. But, when I am trying to learn how to properly analyze positions, I don't understand how memorizing one line of a very specific position helps that.

Not immediately, it's not. 

ratio + L + fatherless + get better at chess + bozo

It depends on the course. Some courses just suck at expaining the moves, it's not chessable's fault, is it.

Once it's imprinted there, it's your job to start seeing it coming in terms of your opponent's intent, or see where you can provoke an opponent into the mating net or trap etc in a forthcoming possible sequence. In doing that your moves become more purposeful and forcing, and you can tell a good trade from a bad trade a lot better. It does start helping you in evaluating positions and candidate moves. The downside is that you can still do all that, fail, move, and then immediately realise you're losing a piece in four forced moves, and furthermore that the position thereafter is a total disaster.

Probably of optimum benefit if you play 1. e4?

memorization.

Chessable was created to help people memorize move sequences, not enhance awareness of structures, plans, &/or themes.

I don't know much about chessable at all