Given a circle, a tangent line is a line that baaaarely touches the circle but doesn't cross it. The single point at which the line and the circle touch is called the point of tangency.
In this picture, A is the center of the circle and B is the point of tangency. Notice that radius AB is perpendicular to the tangent line. This is an important rule: a tangent line to a circle is always perpendicular to the radius to that point.
Often, this piece of information can be used to draw right triangles or rectangles, which then help you solve the problem.