Properly speaking, the doctrine that at least some objects have essences; that is, they have some of their properties essentially, not just because they are described in a certain way (a bishop is essentially in holy orders, yet could be defrocked without ceasing to be himself) but because they must have those properties to be themselves.
You might perhaps have been of the opposite sex, while still being yourself, but might you have been a horse?
Under the influence of empiricism in general and logical positivism in particular, essentialism has been unpopular.
Recently, though, it has enjoyed a revival especially led by Saul Kripke and Hilary Putnam.
C Kirwan, ‘How Strong are the Objections to Essence?’, Proceedings of the Aristotelian Society (1970-71)