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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.

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    Without going into the details it means that your curve will approach the line $y=K$ when $x$ gets very large. – 2017-01-12
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    If you write that as answer I can mark the question as resolved. – 2017-01-12

2 Answers 2

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

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