How many languages exist over a finite alphabet?
The number of possible words is countably infinite, since we can list them in increasing order of length:
$$
\epsilon,a,b,aa,ab,ba,bb,\ldots \\
\epsilon,1,11,111,1111,11111,\ldots
$$
This is why $|\Sigma^*| = \aleph_0$ (to use a more common notation). The set of all possible languages is the set of all subsets of $\Sigma^*$ (known also as the power set of $\Sigma^*$), which by definition has cardinality $2^{\aleph_0} = \aleph$.

If you are unfamiliar with these terms, you need to do some reading on elementary set theory.