to come to know: to learn, perceive, or grasp something so that it becomes part of what you know
At its heart this word is about knowledge that is gained, not knowledge you simply already have. Where the other common Greek verb for knowing points to a fact already settled in the mind, this one points to the moment and the process of finding out, catching on, or coming to understand. That is why it covers learning a piece of news, realizing what is going on, and slowly arriving at deep understanding.
Because the knowing it describes is acquired through contact and experience, it stretches naturally from grasping a fact to knowing a person. When the Bible speaks of God knowing his people and of people coming to know God, this is usually the word, and it means far more than knowing facts about them: it is the knowledge that grows out of a real relationship. The same instinct, that to know someone is to be intimately involved with them, lies behind its use as a gentle way of speaking about the union of husband and wife.
The senses below are not separate words but shades of this one idea of coming-to-know, sorted by what is being learned and how deeply. Context, not the word itself, tells you whether someone is finding out a fact, waking up to a danger, recognizing a truth and owning it, or knowing another person through and through.