I'm studying universal algebra. I have this definiton: given a signature $\Omega$, an $\Omega$-algebra is comprised of a "carrier" for the algebra and an "interpretation" for every operation symbol. The carrier of $A$ is a set (written $|A|$). The interpretation of $\omega\in \Omega$ is a function $a_{\omega}:|A|^{ar(\omega)}\longmapsto |A|$, where ar is the function associating to each operation symbol its arity.
Now, I can't understand the following "equivalent" definition: an $\Omega$-algebra is essentially a carrier $|A|$ and a single function $$a:\displaystyle\sum_{\omega\in\Omega}|A|^{ar(\omega)}\longmapsto |A|$$ in which $\sum$ is the disjoint union operator. The domain is the set of terms which consist of a single operation applied to elements of $|A|$ and the function $a$ evaluates those in $|A|$.
This sounds obscure to me: what actually this functions $a$ do? If the domain is the disjoint union, how can 'a single operation applied to....' be elements of that domain?