A definition -- as opposed to an explanation -- is a lowest common denominator, a single feature common to all members of a set and never found in any non-member. Atheism's LCD is lack of belief in God/Gods (however you define them). There are atheists with a lot more philosophical baggage, and these may be distinguished by adding modifiers the basic "atheist."
You might find the following of interest. None of it is original (all copy-and-paste), although some lacks attribution:
Definition - a statement that specifies the proper application of a term or concept. The defined concept is sometimes called the
definiendum (that which is defined), while the rest of the definition is called the
definiens (that which does the defining). If a definition’s definiens fails to include elements that it should, then it doesn’t provide appropriate necessary conditions, and is too narrow. If it includes element that it should not, then it fails to provide appropriate sufficient conditions, and is too broad. “A bird is an animal that flies” does both. It excludes penguins and includes bats and some insects. Ideally, a definition’s definiens will include both a
genus - the broader class to which a defined concept belongs and
differentia - the features that set the defined concept apart from other members of its genus.
DEFINITIONS
Substantive definitions - primarily focus on what something is. They seek to isolate the essence or substance of the definiendum Ex; Religion - belief in invisible superhuman power together with feelings and practices that flow from such a belief. Two types:
Intensional definition - gives the necessary and sufficient conditions for belonging to the set being defined. For example, an intensional definition of bachelor is 'an unmarried man' or sometimes 'an unmarried man that has never been married'. Being an unmarried man is a necessary condition for both definitions, but not sufficient in the second case, since divorced and widowed would be bachelors by one definition, but not the other.
Definition by
genus and difference is a type of intensional definition, such as 'a miniskirt - a skirt with a hemline above the knee,' or 'bachelor - an unmarried man that has never been married.' Each lists a genus, or larger category to which the definiendum belongs, then limits it to just a subset of the genus. Intensional definition also applies to rules or sets of axioms that generate all members of the set being defined (square number - any number that can be expressed as an integer multiplied by itself). Similarly, an intensional definition of a game, such as chess, would be the rules of the game
Extensional definition - of a concept or term formulates its meaning by specifying its extension, that is, every object that falls under the definition of the concept or term in question. For example, an extensional definition of 'bachelor' would be a list of every bachelor. The term "nation of the world" might be extensionally defined by listing all of the nations of the world, or by giving some other means of recognizing the members of the corresponding class. An explicit listing of the extension, which is only possible for finite sets and only practical for relatively small sets, is a type of
enumerative definition. Extensional definitions are used when listing examples would give more applicable information than other types of definition, and where listing the members of a set tells the questioner enough about the nature of that set.
Extensional and intensional definitions - Wikipedia
Ostensive definition - conveys the meaning of a term by pointing out examples. This type of definition is often used where the term is difficult to define verbally, either because the words will not be understood (as with children and new speakers of a language) or because of the nature of the term (such as colors or sensations). It is usually accompanied with a gesture pointing out the object serving as an example, and for this reason is also often referred to as "definition by pointing"
Functionalist definition - focuses on what something does: Religion - a system of beliefs and practices by means of which a group of people struggles with the ultimate problems of human life).
Operational definition - relies on a process, such as a measurement (temperature – that which a thermometer measures).
