Do you know how to swim? How to play the piano? How to solve a mathematical puzzle? How to paint a picture?
Do you know that twice three is six? That a cat typically has four legs?
Such are questions about knowledge (knowledge-how and knowledge-that).
What does it mean to know something? Is it necessary to know that you know something to know it, or can you know something unknowingly? Such questions are questions about epistemology: the theory of knowledge ("episteme" is "knowledge" in Greek). This is one of the oldest realms of philosophy, and with metaphysics and ethics encompasses most of what modern philosophers think about.
Epistemic naturalists believe that the only way to study knowledge is by an appeal to the natural sciences. For example, neuroscience tells us how we know things. But this in insufficient to answer the questions of epistemology: unless we know what knowledge is first, how can we possibly say what it is scientifically? We need a way to talk about knowledge as it appears.
Immanuel Kant begins his "Critique of Pure Reason" with the phrase "there can be no doubt that all knowledge begins with experience." This is a recognition of the work of empiricists, such as John Locke. John Locke postulated that at birth, our minds are blank slates (or "tabula rasa"). We know this because children, savages, and the mentally disabled do not know things that would be indisputably foundational to knowledge. We have to learn things as simple as "whatever is, is".
David Hume took this further, by separating all knowledge into either "Matters of Fact" (an empirical fact of the world, discovered by repeated observations, like "gravitational attraction draws two bodies together"), or "Relations of Ideas" (truths that are so by the definitions of words, like "a bachelor is an unmarried man"). This, also known as "Hume's Fork", creates a problem. Metaphysical ideas about the nature of reality are not knowledge. That every effect has a cause is not a relation of ideas, but it's not quite a matter of fact, either. We don't just observe causality over and over again: we cannot imagine a world where it is not true.
We could look in the other direction from these empiricists, to the rationalists. These are philosophers who believe that the foundations of our knowledge do not come from experience, but from reason. Descartes is one of these. His argument went thus: when we dream, we do not know that we are dreaming, but when we awake, we know that we were dreaming. Likewise, the world could be formed such that at all times we are like dreamers. For instance, a demon of unimaginable, God-like power, could use its power to trick us into believing that we are seeing the world as it is, when in fact it is a complete and total hallucination. It could trick us into believing that two and two equals five. What, then, in this skeptical state, can we know indubitably, using our reason? Well, we can know that we are using our reason to doubt, and this mental agitation most definitely exists. Cogito ergo sum ("I think, therefore I am.")
Both Hume and Descartes live out a problem that is as old as philosophy itself. Plato, the rationalist, argued that what we can know are the Forms of the world. We know what a table is by its participation in the universal "tableness". My computer is like every other computer in that it has "computerness". All red things are Particular instantiations of the Universal, redness. Aristotle, like Hume or Locke, valued the empirical world. What can be known is things that we can see. At the time that he lived, Aristotle knew everything that could be known, something that nobody in the information age can claim.
Both of these philosophers hearken back to their instructor, Socrates, who "only knows that he knows nothing". Plato, voicing Socrates, is loosely credited for an epistemological view that has shaped two centuries of epistemic thought. He argued that knowledge is an opinion with good reasons for believing it true, also known as the "justified true belief" account of knowledge.
Is knowledge simply justified true belief? What justification is sufficient? Does the truth of a knowledge claim depend on the particular person who is positing it? If someone says "I am a man" or "I am a woman", does the subject of the claim not matter? To what degree should we be pluralistic?
And what about lucky claims, that are justified and true, but whose justification is faulty? For instance, two people are applying for a job. You argue that "the person who gets this job has 35 cents in his pocket". By complete coincidence, both applicants have 35 cents in their pockets, so no matter who wins, you have accidental, lucky knowledge.
There is much more to this subject than I can write here. How did Kant preserve metaphysical knowledge from the ravages of David Hume? Is "every effect has a cause" knowledge? What about the existence of God, or the status of space and time? Metaphysics, formerly known as the queen of the sciences, depends on a solid epistemology to protect it from irrelevancy. Ever since Descartes, epistemology has been known as “first philosophy”.