To deduce is to figure something out based on what you already know. When you see a person crying, it's easy to deduce that the person is sad. Unless they're happy, of course. Sometimes happy people cry.
Derived from the Latin ducere, meaning "to lead," a person who deduces something is "leading" their mind from one idea to the next. Deduction is a noun from the verb deduce: it's what we call something that we learn when we deduce. Sherlock Holmes, the famous investigator created by Arthur Conan Doyle, was a master of deduction. He could deduce from a few small clues all of the facts of a murder case.