The tangent of a parabola is very similar, in spirit, to the tangent of a circle. The tangent of a parabola is simply any line or line segment that intersect the parabola in one and only one point. There are infinite lines that are tangent to any given parabola.
In the picture below, two tangents are shown. Both of the red lines are tangents because they intersect the parabola only once. As the picture shows, there are an infinite number of tangents for any parabola.