Emerging in a time period where America was undergoing a bevy of calls for social reform from a variety of sources, Transcendentalism argued for an injection of emotions into consciousness. In analyzing what was being called for, there is much in way of British Romanticism as a base. Transcendentalists believed that human emotions were worthy of being fully integrated into the lives people led. Thinkers like Emerson were animated by the idea of individuals not following social demands or the "herd" mentality of society at the time, but rather embrace their own sense of uniqueness and distinction in following this path. The individual was able, according to the Transcendentalist, to form their own path, create their own state of being in the world and did not need to suppress their own individual emotional expression in order to assimilate or be deemed as socially acceptable. This becomes the basic idea of "Self- Reliance," in its assertion that individuals can be their own barometers for what is good and right, as the need to be dependent on society to determine can be less.
Transcendentalism was a philosophy that became popular among American elites in the 1830s and 1840s. When it comes to this particular essay, the main aspect of transcendentalism is the idea that all people have the right and the duty to decide for themselves what is right and what is wrong. The Transcendentalists believed in listening to their own consciences and not to what society said.
You can see that in this essay, for example, where it says that anyone who wants to be a man must be a nonconformist. This is the main idea of the essay -- if you want to truly be a human being you must follow your own conscience rather than following society's values.