Questions of equality and equivalence are of fundamental importance in mathematics and computer science. In everyday use we are usually comfortable with a vague definition of equality, but in programming for example, two objects may be identical in one instance and different in another. This is usually a great source of confusion for inexperienced programmers. In mathematics, equality has multiple meanings and uses and even basic subjects like high school geometry introduce the notions of similarity and congruence that represent two different levels of equality.
Of course, equality and equivalence are also part of the branch of philosophy called ontology. In the following classic animation, John Weldon presents the topic as a fun thought experiment that asks the question: what does it mean to be? Watch it and be amazed by the philosophical nuances of existence.