An intro is the opening section of a piece of music, usually before the singing begins. Often when you hear a pop song's intro, it's so familiar that you'll recognize it immediately.
There are intros in popular music, as well as other musical styles, and a book or essay can have an intro as well, a few paragraphs or pages setting up the ideas to follow. Another kind of intro is when you formally present, or introduce, a person to a group or an individual. In fact, intro is a casual shorthand for introduction, from the Latin introductionem, "a leading in."