An object has a distinguished identity, a changeable state and some well-defined behaviour. Similarity between a collection of objects can be captured in terms of a class definition.

object, v
7. a. intr. To state an objection or adverse reason; now often in weakened sense: To express or feel disapproval, to disapprove.
object, n
2. Something ‘thrown’ or put in the way, so as to interrupt or obstruct the course of a person or thing; an obstacle, a hindrance. [Obsolete].
3. a. Something placed before the eyes, or presented to the sight or other sense; an individual thing seen or perceived, or that may be seen or perceived; a material thing ...
b. Something which on being seen excites a particular emotion, as admiration, horror, disdain, commiseration, amusement ...
4. That to which action, thought, or feeling is directed; the thing (or person) to which something is done, or upon or about which something acts or operates

-- Oxford English Dictionary, 2nd edn

Object-oriented programming focuses on objects that persist and yet change over time.
Since animals persist and yet change, they belong conceptually at the object-oriented level, and we say that Dog is a 'subclass' of Mammal, and Mammal is a 'subclass' of Vertebrate. However, since numbers do not change, they belong at the functional level, and we say that Nat is a 'subsort' of Int, and Int is a 'subsort' of Rat. Thus both functional and object-oriented levels have an inclusion relation, respectively expressed as subsort and subclass, with the class of dogs included in the class of mammals, and the set of natural numbers included in the set of integers. Both relations are partial orderings under set-theoretic inclusion.

-- Goguen & Meseguer. Unifying Functional, Object-Oriented and Relational Programming with Logical Semantics. 1987

An object has a set of operations and a state that remembers the effect of the operations. Objects communicate by sending each other messages to perform operations. Object may be contrasted to functions, which have no memory. Whereas function values are completely determined by their arguments, an object may learn from experience, its reaction to an operation being determined by its invocation history.

-- Wegner. The Object-Oriented Classification Paradigm. 1987