What is a "formal definition" of a set? I'm to find a formal definition of a certain set, but I'm unsure what it means by "formal definition" (in relation to Discrete Maths)

A quick google search didn't seem to help me much. Can anyone provide me with an example of a set, and a formal definition of it?

Update: I can't really give much more detail about the question itself because it's a graded assignment. (I do study Computer Science, and the Discrete Maths course I'm doing is run by the computing department). It gives a set of vague conditions for a set A, then asks to write down a formal definition of a set B which contains all such sets.
As set is one of the things set theory talks about, so for ZFC set theory for example it is one of the sets guaranteed (or at least allowed) to exist by one or more of the axioms of ZFC. The formal definition of a specific set would consider in a proof of the existence/construction of the set in question. Most of the axioms come with the introduction of special notations for the set they guarantee to exist (provided the set is also unique). Thus for example


$\{a,b\}$ denotes the set guaranteed to exist by the Pairing Axiom for given sets $a,b$
$\mathcal P(a)$ denotes the set guaranteed to exist by the Power Set Axiom for a given set $a$
$\bigcup a$ denotes the set guaranteed to exist by the Union Axiom for a given set $a$
$\{\,x\in a\mid \phi\,\}$ denotes the set guaranteed to exist by the instance of the Axiom Schema of Comprehension for a given set $a$ and predicate $\phi$
$\{\,F(x)\mid x\in a\,\}$ denotes the set guaranteed to exist by the instance of the Axiom Schema of Replacement for a given set $a$ and function $F$


Combinations of these allow the formal definition of quite complex sets.
As a shortcut, one often uses $\emptyset$ for $\{\,x\in a\mid x\ne x\,\}$ where $a$ is an arbitrary set (which is guaranteed to exist), or $\omega$ for a specific (namely minimal inductive) constructabel from a set that is guaranteed to exist from the Axiom of Infinity. Other constant symbols for specific sets are often introduced and can readily be used as abbreviations (for example, I won't write down a completely expanded definitoin of a set widely known as $\mathbb R$) in such formal spevcifications.
In most cases, you'll write down your formal definition of a set either the Comprehension or the Replacement way.
From the Collins Dictionary of Mathematics: 

set: a collection, possibly infinite, of distinct numbers, objects, etc., that         is treated as an entity in its own right, and with identity dependent only upon its members.