I do not quite understand what destructive cancellation is, can someone explain it please? I have been given this example 2.0013−2.0005=0.0008. The destructive cancellation is the large common value, here the 2, that disappears. 

Suppose $x$ and $y$ are known to five significant figures: $x \approx 2.0013$ and $y \approx 2.0005$. This means that $2.00125 \le x \le 2.00135$ and $2.00045 \le y \le 2.00055$ (some of the $\le$ signs can be replaced by $<$ signs, but exactly which ones depends on the rounding mode used).
But then if $z = x - y$, all we can confidently say about $z$ is that $0.0007 \le z \le 0.0009$, so $z$ is not even known to $1$ significant figure.
Destructive cancellation is this catastrophic loss of significant figures that can occur when subtracting two almost equal floating-point numbers.
