The Essential Writings are the published theories and explanations of Jacques Lacan, mostly revolving around his Freudian themes, including what he called the mirror stage, a period of time during developmental psychology during which a small child learns to self-perceive, causing the development of an ego that is the construct of imagination, not the byproduct of natural, unguided processes. The effect is that adults, from Lacan's perspective, are stuck navigating the world with a sense of self that is primarily an illusion, constructed during the time when they were a child mimicking others' behavior and demeanor.
Another major feature of these writings is the return to Freudianism. Many of Freud's theories were reconstructed by Lacan, making Lacan's views something of a variation on a theme of Freud's. That just means that many elements of their worldview are strikingly similar, but even the ideas they agree on, they disagree on still, because they're each interpreting the mind through their perspectives. Although many scholars found issues with Lacan's adoption of Freudian ideas, but a reader who likes Carl Jung or perhaps the famous developmental psychologist, Piaget, will likely resonate with Lacan's point of view.
Here's the basic idea of the mirror stage, the major contribution of these writings: Lacan believes that when a young child, perhaps even an infant, looks into a mirror, they find themselves tasked to understand their own reflection, and once they know what they look like, there starts to exist in their mind an ego that is a constructed, specular image of the real child based on their physical appearance. In other words, they imagine a version of their self which aids them in the speculative business of decision making, prioritizing, and even motor skills and physical behavior.
Basically, Lacan's writings explore this question: What is the effect of reality on the development of the mind? Because many of his points depend greatly on subconscious processes, his works have been regarded with mixed, polarized reactions, but his contributions to psychology shouldn't be understated. Lacan is a truly influential writer, and these writings are designed to offer a cohesive collection of those ideas.