PAC Learnability - Notation
The explanations are as follows:


$m_H:(0,1)^2 \rightarrow \mathbb N$ is a similar notation to $f:R^n\rightarrow \mathbb N$ which means it takes a n-dimensional input consisting of real numbers only. In the case of PAC learning the input is 2 dimensional consisting of numbers between $0$ and $1$ only which stand for values of $\epsilon, \delta$ respectively.
The integer $2$ as explained above is the dimension of the input vector.
$\rightarrow \mathbb N$ means mapped to natural numbers. In case of PAC learning that for each value of $(\epsilon, \delta)$ a function $m_H$ maps it to natural numbers, simply put $m_H(\epsilon, \delta) = $