If you memorize something you know it by heart. When you were a little kid, you were probably asked to memorize “The Pledge of Allegiance,” meaning you could recite it from memory with no cheat sheets.
To memorize something is to get it into your memory, but it usually implies you’re learning something more complex than a new acquaintance’s name or the time of your next dentist appointment. People typically memorize things like multiplication tables, the periodic chart, Shakespearian quotes, lines for the community theater play, and their nine hundred different online passwords. There are many systems that people use for memorization: flash cards, association, color coding, and even sleeping with the book under their pillow.