One of the classical DefinitionsForOo; one which is often accused of being CeePlusPlus centric. A language supports OO programming if it has:
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Polymorphism; in this context this really means SubtypePolymorphism. As pointed out below, there are many other types.
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Encapsulation; there are means to segregate an object's interface from its implementation. This may be enforced by the language (as in CeePlusPlus and JavaLanguage) or by convention (as in PythonLanguage and CommonLispObjectSystem)
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Inheritance; reuse of base classes to form derived classes. Some object to this, as other mechanisms exist (interface inheritance, delegation, structural typing) to implement subtypes.
In most ObjectOriented Languages: Polymorphism = Encapsulation + Inheritance
But InheritanceBreaksEncapsulation.
Is PolyMorphism the reason for ObjectOrientation to exist?
No, OO exists because it's a convenient way to structure code and modularize programs. Polymorphism is a key benefit, but not the only one.
There are other ways to achieve Polymorphism, namely ParametricPolymorphism (STL = StandardTemplateLanguage) and Generics (TheRightWayToImplementTemplates).
Generics are ParametricPolymorphism. While JavaGenerics and CppTemplates and DynamicTyping all go about it the same way; they all are ways of implementing ParametricPolymorphism