Philosophers have been accused of using words in very unconventional ways, which is confusing for people who aren't philosophers. There's a reason they do it, though. They do it for the sake of clarity. Language, the way it is commonly used, can be very ambiguous. Since philosophers are trying to address hard questions that require a lot of precision and careful thinking, they want to define their terms in precise ways so they can understand each other and communicate clearly. This requires them to give very precise definitions to the words they use. It doesn't matter whether the definitions they give are common or not. What matters is that the reader understands what they are saying. As long as you understand what somebody means by the words they are using, you can figure out what they are trying to communicate with those words.
Words and their meanings didn't just fall from the sky. A word doesn't mean something because the dictionary says so. It's the other way around. The dictionary is an attempt to capture what words already mean. What determines the meaning of words is just how they are used. Since any given word might be used in multiple different ways, there are some ways that are more common than others. Dictionaries attempt to put the most common uses first and the least common uses last.
In the case of the word, knowledge, the definition philosophers typically use may be unusually precise compared to the way most people would definite it, but it's not an arbitrary definition that's peculiar to philosophers. Rather, it's a definition that was arrived at in an attempt to capture the common use. Let me try to show that by asking some questions.
Would it make sense to claim that you know something if you didn't even think it was true? Probably not. Wouldn't it seem odd to say, "I don't think birds of a feather flock together, but I know they do"? I suspect that would seem odd to you. At a bare minimum, then, before you can know something, you have to at least believe it to be true. To "believe," just means to think something is true.
If I believe something, is that enough to claim that I know it? We have already established that belief is necessary for knowledge, but most of us would acknowledge that belief is not sufficient. Something more is needed. After all, I might believe something and be wrong about it. People believe all sorts of things that aren't true. You can't know something is true if it's not true. So at minimum, before you can know something, it first has to be true.
Now we've shown that to have knowledge, you need at least two ingredients. You need it to be true, and you need to believe that it's true. But are those two things enough?
Well, consider a situation in which somebody, for no reason at all, or for some erroneous reason, comes to believe that there is life on Jupiter. Up until now, no discovery of life on Jupiter has been made, and no chemistry or light on Jupiter has given us any reason to think there's life on Jupiter. But then suppose that years down the road, a probe sent into the atmosphere in Jupiter found that, in deed, there is mocrobial life floating in the atmosphere of Jupiter. If that were the case, then the person who believed there was life on Jupiter would have been right all along. He had a belief that turned out to be true. Would it be fair to claim that he knew that there was life on Jupiter?
I hope you said no. The way we commonly use the word, knowledge, seems to entail that he didn't have knowledge. Rather, he just made a lucky guess, and happened to believe it. What is missing? Well, if he just arbitrarily believed something he made up, the missing ingredient seems to be justification. If he had concluded that there was life on Jupiter because he performed some spectroscopy on the planet and discovered chemicals in the atmosphere that could only be created by living organisms, then he would have some justification for believing there was life on Jupiter. Or, if he had been part of the team that sent a probe to Jupiter, and he was privy to the data the probe sent back indicating that it found life on Jupiter, then he would by justified in beliving there was life on Jupiter. Then we might say he knows there's life on Jupiter.
Now, we have established that knowledge requires (1) belief, (2) truth, and (3) justification. That is why the typical definition philosophers use for knowledge is "justified true belief." That has served as a satisfactory definition for knowledge in most cases.
Being the persnickety people that good philosophers are, though, even this definition has been probed for its accuracy. Just as in the scientific method, we test hypothesies by trying to falsify them, so also in the case of philosophy, we test ideas by trying to think of counter-examples. A philosopher named Edmund Gettier came up with some counter-examples to the definition of knowledge as justified true belief. The issue he raised has become known as "The Gettier Problem" since there is no concensus on the resolution.
A counter-example to knowledge as justified true belief would be a scenario in which all three ingredients are present, but we still don't think the person has knowledge.
When I was in middle school, I had a friend named Chad who had a girlfriend named Wendy. One day, as a joke, I told Chad that Wendy said she was going to break up with him. Chad believed me because he didn't have any reason to think I'd lie about something like that. Seeing the look on his face, I felt bad and immediately told him it had been a joke. He went about his merry way. The next day, Chad came at me angry for lying to him. It turned out Wendy really did break up with him, and he was mad at me for claimimg that it had been a joke when it was actually true.
Notice that when I told Chad that Wendy was going to break up with him, he had all three ingredients for knowledge. (1) He believed Wendy was going to break up with him, (2) he was justified in believing Wendy was going to break up with him, and (3) it was true that Wendy was going to break up with him. Yet because I was joking, most of us would probably agree that Chad did not have knowledge. I wasn't reporting to Chad anything that I actually knew. It was just a coincidence that I happened to be right. This scenario, then, serves as a counter-example to knowledge as justified true belief. It appears that something else was missing. What was it?
Here, philosophers give different answers. Some answers involve tweaking or qualifying the criteria of "justification" in some way. What exactly is justification? Will any ole justification do? Other answers involve adding a fourth criteria. What other ingredient is required for knowledge?
Since Gettier problems in real life are very exceptional, I think that pragmatically speaking, we can just ignore them. The definition of knowledge as justified true belief is a good enough rough definition to cover most real life cases. But when it comes to arguing the nitty gritty details of the things weirdos like you and I like to talk about (including the topic of epistemology), it might be useful to tackle the Gettier problem.
While I haven't read a whole lot of literature on how other philosophers have tackled this problem, my own unrefined view is that whatever the justification for our belief is, it must be a proper justification. That is, the justification must actually bridge the gap between the belief and the reality. There has to be a connection between the two. There is no connection between the reality of Wendy breaking up with Chad, and Chad's belief that Wendy would break up with him since I just made it up. If Wendy had told me she was going to break up with him, and I had told Chad, then there would have been a bridge from the reality to the belief. In that case, Chad would have a proper justification for his belief that Wendy would break up with him. That would give him knowledge.
While I am happy to define knowledge as justified true belief without going into the Gettier problem, if I had to nail it down more precisely, I would just add the "proper" part along with the explanation. My more persnickety definition of knowledge would be "properly justified true belief."
How would you deal with the Gettier problem? What is the missing ingredient for knowledge that is left out by the usual definition?