The point of tangency is the point at which a line touches an ellipse or circle, assuming that the line only makes contact at one point. The line running through the point of tangency only has that one point in common with the circle or ellipse, and it is called a "tangential" line with respect to that shape.
Other lines intersect a circle at two points instead of one, and these lines cut the circle at two different places forming a secant. Some mathematicians refer to the tangent as the limit case of a secant; as the secant gets further from the circle's center, the two places where the line intersects with the circle gradually merge into one point, and at that point the line becomes tangent to the circle.
In situations that involve two circles, the external tangents run along the edges of both circles without crossing between them, while internal tangents apply to slightly different points allowing the lines to run between the circles. For circles that make contact at one point, there is an extra tangent running between them, actually tangent to both. When one circle lies inside the other, there are no common tangents. A line that is a tangent to the inner circle would function as a secant for the outside circle.