Imagine flinging a yo-yo in a circle around your head. You let go, and it flies off in a straight line towards your mom’s favorite ceramic figurine.
Tangent lines have caused you grief, yet again. In this case, the tangent is the line formed from the yo-yo's point of release to the point of impact. A tangent is a straight line that touches a point on a graph without actually crossing the graph at that point. They’ll show up most often when we talk about slopes and derivatives. Yes, you also saw these in trigonometry and geometry. They're pretty useful, but not for reconstructing ceramic figurines. Sigh...