know
To have information or understanding about something in your mind.
To know something means to have information or understanding about it stored in your mind. When you know your best friend's birthday, you can remember it without checking a calendar. When you know how to ride a bike, you've learned the skill and can do it. When you know that water freezes at 32 degrees Fahrenheit, you've learned that fact and can recall it.
There's an important difference between knowing something and merely believing it. You might believe your team will win the championship, but you don't know it until the final game is over. Knowledge requires certainty or strong evidence, while belief can exist with uncertainty or hope.
The word know also means to be familiar with a person or place. You might know your math teacher well after having her for a whole school year. You know your own neighborhood better than a visitor would. This kind of knowing comes from experience and time spent together.
When someone says “I know!” they're often claiming to understand or agreeing enthusiastically. If a friend complains about a difficult assignment and you reply “I know!” you're showing you understand exactly what they mean because you've experienced it too. People also use know when they're certain about something: “I know I put my homework in my backpack this morning.”