What are esoteric schools? Why - and where - do they exist? How they achieve their stated goals?

A good, starting point is the succinct booklet by American Theosophist Gottfried de Purucker titled: The Esoteric Schools (extracted from his book: The Esoteric Tradition, 1935).

I have encountered - and been a student of - a few esoteric schools. My understanding is that esoteric Schools are special, unique places where a human being can learn immortality through the acquisition of specific knowledge and methods aimed at developing latent faculties and the inner soul, i.e. that part of the self connected to God, or the whole (different traditions use different names).