knowledge
Understanding and facts you learn and can use.
Knowledge is what you understand and remember after learning something, information you truly grasp and can use. When you have knowledge of fractions, you don't just recite “one half equals two fourths.” You understand why they're equal and can solve problems with them.
Knowledge comes from experience, study, observation, and thinking carefully about what you learn. A chef develops knowledge of how flavors work together by cooking hundreds of meals. A mechanic gains knowledge of engines by fixing them and understanding how the parts interact. You build knowledge of your neighborhood by exploring it, not just by looking at a map.
People sometimes confuse knowledge with information. Information is just data: facts, numbers, or descriptions. Knowledge is information you've processed and connected to other things you know. Reading that Abraham Lincoln was born in 1809 gives you information. Understanding how his childhood shaped his views on democracy and equality: that's knowledge.
The phrase to my knowledge means “as far as I know” or “based on what I understand.” If someone asks whether the library is open on Sundays and you reply “Not to my knowledge,” you're saying you don't believe it is, though you're not completely certain. Knowledge isn't always complete or perfect, but it's more reliable than a lucky guess.