As a pure definition, "Self" is the distinction between "I" and "We." Self is seen as a identifier showing a single person or consciousness as unique, not part of a herd or collective. Self is seen in humans and some animals, and it is significantly not seen in other animals, such as the simple organisms that make up coral -- these are called Zooids.
In human psychology, the theory of Self is indeterminate; there is no "Self Organ" that houses individual consciousness, and while multiple theories have placed the self in certain parts of the brain, studies of accident victims show an extraordinary range of response. There is no single hypothesis to define "The Unique Self" in every case, but some general information can be deduced from theory and experiment.
First, the concept of "I" or the Ego is significant in most modern psychological theory. The "I" that we refer to when we desire something or express an opinion is differentiated from all other "I" creatures in that we consider our rational thoughts to be the personification of a consciousness. We are not expressing the views of every "I," but only our own single "I."
In another sense, some theorists believe the ability to reason in an abstract sense to be proof of Self. Humans can lie, invent, form hypotheses, and enjoy random stimuli; most animals can only relate to the reality that is directly affecting them. This ability for abstract thought separated humans from animals, and also separates humans from each other; some people cannot reason abstractly, having an entirely literal mindset, while others cannot reason literally. The difference between each person and their personality is an example of Self as it relates to other, unique Self constructs.
Finally, our mutual understanding of human uniqueness allows humans to rely on general principles of "humanity" while differentiating their separate desires. Some religions believe the Self to be an illusion, and that every "I" in the world is actually part of a greater intellect. Others believe that his or her own "I" is the only thing that is unique, with all others simply constructs of their own imagination.
The Self as justified by experience is far more valuable than the Self justified by theory. Perception of the Self can be harmed by excess entitlement, or bolstered by personal achievement. With no hard facts regarding the placement or "reality-based" existence of the Self, it is up to each "Self" to decide what theory is best suited.
In one small word, I would say it is the "I" in me. This smallest and simplest one letter word plays havoc and effects my relationship more severely than anything else.
To put it straight, it is the "ego", control it and you have no problems.
It is surely not the self-esteem or self-respect, if it is gone, one is completely finished.