In our physical world, an object is a tangible "something" upon which our senses can feel and that which we can manipulate. In software development, objects are not tangible something rather they are a models of something that can do certain things and have certain things done to them. Formally,
an object is a collection of data and associated behaviors.
What, then, is object-oriented?
Oriented simply means directed toward or an inclination toward. So when we say object oriented it means, "functionally directed towards object".
This allows us to model complex systems via a collection of objects manipulating their data and behaviors.
Highly related concepts under the same general object-oriented umbrella:
Analysis, design and programming actually are just stages of software development. Object-oriented is simply a style of software development.
Object-oriented analysis
Object-oriented design
Object-oriented programming
as usual, the real world is much murkier.
Disclaimer: this is a summary of section 1.1 from the book "Python 3 - Object Oriented Programming: Dusty Phillips", the content apart from rephrasing is identical, most of the equations are from the book and the same examples are treated. All of the equation images were screenshot from generated latex form.