What is an asymptote?

Question

I'm a student of Zoology having class XII Maths background.

I stumbled upon asymptote while studying S-shaped growth form in ecology. I tried to google it up and found wikipedia define it in the following way:

In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as they tend to infinity.

I don't get the last part. What does it mean?

NOTE: K (carrying capacity) is the asymptote in the diagram.

Answer 1

Without going into the details it means that your curve will approach the line $y=K$ when $x$ gets very large.

Answer 2

Intuitively, in your example in the diagram, it means that the number of individuals will approach $K$ as time increases (becomes very large).