When evaluating or constructing an argument, one typically defines a domain, that is, the set of all elements being considered in that specific problem or context. This is also referred to as the domain of discourse of universe of discourse. The domain can be restricted to a certain kind of thing, such as all animals or all people, or the domain can be unrestricted so as to include literally everything.
Members of the domain are specifically named things, and they are represented by individual constants such as $a,b,c$ or any of the first $23$ letters of the alphabet. A variable, such as $x$, represents an arbitrary, unnamed element from the domain.
An open sentence, or propositional function, becomes a statement with a definite truth value once every variable therein is either $(1)$ substituted with a constant from the domain or $(2)$ bound to a quantifier. You can substitute any constant you wish to produce such a statement, but the choice of constant is usually dictated by the specific problem or argument you're working with. In other words, you may require a specific constant from the domain because that constant appears in other statements, and you may need a subset of statements discussing the same constant in order to apply a desired inference rule. For example, take the argument
$\forall x [Fx \to Gx], Fa \vdash Ma$
where
$F:$ ___ is a folk singer.
$M:$ ___ is a musician.
$a:$ Alice
In general, the choice of domain should consist of all and only those things capable of possessing the relevant properties. So here the domain is appropriately defined as the set of all people because all folk singers and all musicians are people, and only people can be folk singers and musicians.
Note that one can apply universal elimination to $\forall x [Fx \to Mx]$ to obtain $Fb \to Mb$ where $b$ is Bob, and this would result in a perfectly acceptable statement, that is, "If Bob is a folk singer, then Bob is a musician." However, if I'm trying to prove the argument, then obtaining a statement about Bob is not helpful because the argument is about Alice. Among all constants I could choose from, I prefer to instantiate with $a$ corresponding to Alice so that I can obtain $Fa \to Ma$ and derive the conclusion $Ma$ via the inference rule known as Modus Ponens.
