I am reading the textbook Contemporary Linguistic Analysis by William O'Grady ninth edition. The text makes the claim that "grammatical knowledge is subconscious". They submit that most people can't explain the meaning of "or" in differing contexts, therefore the knowledge of its actual use is in our subconscious. Using this logic, the fact that I can't explain what happens when I press buttons on a microwave but I know that the input 1-0-0-start will microwave for one minute would mean the low level knowledge of how a microwave works therefore exists in my subconscious. Clearly it does not. Are they saying it does? Should O'Grady not actually state that our knowledge of grammar is often of high level understanding instead of in our subconscious?
Like TKR has already said, I believe it’s mostly a terminological preference.
I don’t really want to discuss here what it means “to know a language” in linguistic research, i.e. not something what linguistically naïve (untrained) people may think. Tons of research have been written on this; if you’re interested, you can start with Andrew Mills' "Knowledge of Language" in the Internet Encyclopedia of Philosophy (it's scholarly and peer-reviewed).
Nor do I want to start a philosophical discussion of what knowledge is – you can read a review article "Knowledge" by Stephen Hetherington or "Knowledge How" by Jeremy Fantl, among many, many others. Why not check out "The Language Instinct" by Steven Pinker then?
When we talk about knowledge of (a) language, the following descriptors are commonly used: implicit, subconscious (and sometimes even unconscious), or tacit. This list is by no means exhaustive.
The idea is that a non-linguist (most of language users) does not understand how they learned their language (“I just picked it up from my parents”) - so no formal/explicit training was necessary to learn your L1, how they can use (“Come up with a thought and open your mouth!”), nor can they teach their language to anyone else, without proper training (“What’s the difference between "for instance" and "for example?”). In other words, I can use a language (or, in common, non-technical parlance, I “know” it) but I don’t understand (=know) how I do it, or, as Dr William O'Grady wrote in the textbook he also edited,
"Speakers of a language know what sounds right and what doesn't sound right, but they are not sure how they know it."
This kind of knowledge is - alas! - inaccessible to language users but, on the other hand, it is the object of serious study by linguists.
There are two kinds of knowledge, conscious and subconscious. Some knowledge about language is conscious, for example you may consciously know that the English word "father" is derived from the same Indo-European root as "paternal" (the latter having come through Latin, the former having come through Germanic). You may consciously know that we negate sentences with "not". These are facts about language data. O'Grady and William are obliquely talking about the underlying mental mechanisms that cause overt language behavior, which is a special kind of "knowing", similar to your knowledge of how to walk: it is a thing that you do automatically. Another kind of subconscious knowledge is "naming", the ability to classify thing according to some "definition". Typically, people who see dogs can correctly say "that is a dog", but they cannot correctly state the necessary and sufficient conditions for a being to be labeled as a dog – because they have internalized an ostensive definition of the term. People also can't explain how they can identify a thing as "red", but they can (unless they literally cannot). That is, they have an internal knowledge state that allows them to classify visual stimuli, but they do not consciously know what that internal state is.
In your microwave example, you don't even know at any level what the underlying mechanism is: you have no knowledge.
The microwave analogy is irrelevant: when you use a microwave, you don't need to have any knowledge of how it heats your food, because it's the microwave that is heating the food, not you. When you produce language, on the other hand, you do so unassisted, so any knowledge required for language production must exist in your brain. In most cases, speakers are unable to consciously articulate such knowledge, so it can be aptly described as subconscious.
This is no different from what you describe as "intuitive knowledge" in your comment on user6276's answer. As you say, "Walking is not something one does automatically, it is practiced, failed at and eventually a person can do it" -- the same is true of language. Whether you call this intuitive knowledge, subconscious knowledge, or higher-level understanding is a matter of terminological preference.