The larynx (or "voicebox") is an very complicated structure of bone, cartilage, and muscle that sits at the top of the trachea or windpipe. The "Adam's apple" in adult males is the front part of larynx.
The intricacies of the larynx aren't relevant here. What is important for basic phonetics is that the larynx houses and controls the vocal folds -- often called the vocal cords, but "folds" is a more accurate description of what they're actually like. The vocal folds are two flaps of tissue stretched across the opening to the windpipe. They may be opened wide (as they are when you're breathing), closed tightly (as they are when you're swallowing or lifting heavy objects), or they may vibrate against each other (creating the source of sound we think of as our "voice").
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The opening between the vocal folds (when it exists) is called the glottis.