Question

What does axis of symmetry of a parabola mean

Answer 1

The  axis of symmetry of a parabola is a straight line which divide graph of parabola in two symetric branches.

Answer 2

If you had a piece of paper in the shape of the parabola, the axis of symmetry
is the line on the paper where you could fold it, and the two edges would exactly
come together.  It's the line right down the middle of the parabola.