In philosophy,

• “ontology is the study of being or existence. It seeks to describe or posit the basic categories and relationships of being or existence to define entities and types of entities.”¹⁾

In modern computer science and information science basic definitions consider an ontology to be:

• “a data model that represents a set of concepts within a domain, and the relationships between those concepts”²⁾
• “an explicit specification of a conceptualization.”³⁾
• “an explicit formal specification of the terms in the domain and relations among them”⁴⁾

In more details, an ontology can be described as:

• a formal explicit description of concepts or classes in a domain of discourse, with
• properties of each concept describing various features and attributes of the concept (slots, roles or properties), and
• restrictions on concept slots (facets or role restrictions).⁵⁾

An ontology has the following properties:⁶⁾

• it is used to reason about the objects in a domain;
• specifies the classes of concepts and their relations at a higher level than relevant to the domain;
• captures the intrinsic conceptual structure of a domain;
• forms the hearth of the knowledge representation within a domain.

An ontology can be used to:⁷⁾

• share common understanding of the structure of information among people or software agents
• enable reuse of domain knowledge
• make domain assumptions explicit
• separate domain knowledge from the operational knowledge
• analyze domain knowledge

You can follow this brief guide or a more detailed description with examples: Ontology Development 101: A Guide to Creating Your First Ontology.