Have you ever driven from one place to another on "autopilot" or caught a ball without thinking? If I ask you what 2 + 2 is, does the answer appear in your mind instantly?
These are examples of doing something almost without thinking - not always using muscles, but still a kind of muscle memory. When we do the same thing enough times, we get so good at it that it no longer requires conscious effort to do.
The key to learning a new skill is to break it down into layers. Learn the bottom layer, and only progress to the next layer when the previous has become muscle memory. Learning is like lasagne.
Think about learning elementary maths. First, you learn how to count, then you learn addition and subtraction, then you learn multiplication and division, and so on. These are the first few layers.
It's obvious that you can't learn how to add or subtract before you learn how to count. It's less obvious that you can't quickly and accurately add and subtract until you have memorised adding and subtracting all the pairs of numbers less than 10. For example, instinctively knowing 5 + 7 = 12, or that 2 + 4 = 6. As people become better at mental arithmetic they often develop muscle memory for this on their own, but, because it often isn't taught explicitly like multiplication tables, you'll find some children still adding on their fingers years after they were introduced to addition.
Learning systems for most skills have evolved to build layers of muscle memory through repetition. We learn the alphabet off by heart, we memorise multiplication tables, and in almost every sport we drill foundational movements thousands of times until we can do them subconsciously. Trying to move to the next layer before mastering the previous leads to slower learning and lower success.
What I've said so far might sound obvious. Everyone already knows that you need to master the basics of a field before progressing to more complex tasks. What's less obvious is that the sign of mastering a layer is when it becomes muscle memory - not when you can adequately perform tasks. Something even less obvious is the mechanism that forces us to learn this way.
It's well known that humans cannot multi-task. The caveat that's often missed is that our conscious mind can't multi-task, but we can multi-task on things that we have muscle memory for. We can have a conversation while driving, or solve 3 Rubik's cubes while juggling them. Being able to complete a lower-layer task without consciously thinking about it frees up your conscious mind to process the next layer. For example, when learning a new language, adults will initially translate foreign words to their native language while constructing sentences. This is their conscious mind attempting to both manage vocabulary and sentence construction at once which is slow and error-prone. Over time vocabulary becomes muscle memory, meaning they understand the meaning of foreign words immediately, and the conscious mind is free to focus on constructing the right sentence.
Next time you're learning (or teaching) something, try to see the lasagne. Ask yourself what the layers are, and if you've truly mastered the previous layers. Identifying gaps in muscle memory is a high leverage way to improve your overall proficiency in the skill because it affects every layer above it.