An academic definition of self esteem is available at the website of the University of Maryland. A more concise definition is available at the Merriam-Webster website. Here, self esteem is defined as "a feeling of having respect for yourself and your abilities."
The University of Maryland website goes into more depth, defining self esteem as a measure or scale of self worth. In other words, self esteem can be either positive (high) or negative (low).
A person with high self esteem has a positive conception of their value, while a person with low self esteem has a negative conception of their value. Having high self esteem is distinct from being egotistical, which is a state of arrogance or conceit and, moreover, of considering other people to have low or negative value.
As a measure of self worth, self esteem may be quantified through psychological assessment. One such assessment is the Rosenberg Scale. Participants are asked to rate their agreement with each of ten statements on a four point scale, from "strongly agree" to "strongly disagree." Statements include "I am able to do as well as most other people" and "I certainly feel useless at times."
Once the answers have been scored, the respondent is assigned a self esteem rating between 0 (lowest self esteem) and 30 (highest self esteem). However, this rating is not constant and is subject to change with life experience.