An Entity is an independent and unique item that can be defined. When we speak of an Entity, we normally speak of some aspect of the real world which can be distinguished from other aspects of the real world. An Entity may be a physical object such as a house or a car, an event such as a house sale or a car service, or a concept such as a customer transaction or order.
Although the term Entity is the one most commonly used, we should really distinguish between an Entity AND an Entity Type. An Entity Type is a category. An Entity, strictly speaking, is an instance of a given entity type. There are usually many instances of an Entity Type. Because the term Entity Type is somewhat cumbersome, most people tend to use the term Entity as a synonym for this term.
Entities can be thought of as nouns. Examples: a computer, an employee, a song, a mathematical theorem.
A Relationship captures how Entities are related to one another. Relationships can be thought of as verbs, linking two or more nouns. Examples: an owns relationship is between a company and a computer, a supervises relationship is between an employee and a department, a performs relationship is between an artist and a song, a proven relationship is between a mathematician and a theorem.